I know I can look this up, but the short answer for a device–it stores energy which can be discharged at will–works for both.
I don’t know what the few words are I can add to make the distinction.
A capacitor discharges it’s energy all at once, then recharges. A battery releases its energy over time.
Do you want an answer in terms of fundamental principles, or in terms of use?
In fundamental principles, a battery stores energy as chemical energy. You start with a couple of metals (like copper and zinc) in an acid or some other material when it’s full, and end up with a sludgy mix of metal compounds when it’s drained.
A capacitor, meanwhile, stores energy in electric fields. No chemicals change, and nothing moves except electrons. One consequence of this is that, unless a capacitor is completely destroyed (which can happen), they don’t really wear out like batteries do.
In practice, there are three main differences: In batteries’ favor, they can (currently) store a lot more energy than capacitors can (but capacitor technology is advancing insanely quickly, and the time will come when that won’t be true any more). And they also have a much better discharge curve: A 12-volt battery, for instance, will continue to produce nearly 12 volts for its entire life, until right at the end when it drops suddenly. A capacitor, meanwhile, will continually dwindle down to 0 volts as it discharges.
In capacitors’ favor, however, there are limits on how quickly a battery can be charged or discharged. Well, strictly speaking, there are limits on capacitors, too, but the battery limits are much harsher. A camera flash, for instance, uses a capacitor to build up energy: You fill up the capacity over a span of several seconds (as fast as you can get the energy out of the battery), but then discharge it in as short a time as it takes to light up the flash.
A capacitor stores energy in an electric field. A battery stores energy in chemical bonds.
A simple capacitor is just two sheets of metal with a gap between them. Charge up the plates, and the energy is stored until you discharge them. Real world capacitors typically have some sort of electrolyte between the two plates, and your typical electrolytic capacitor is often a sheet of foil with electrolyte goo all wrapped up into a cylinder. The goo actually functions as one of the electrodes as well as being the electrolyte in some versions.
A lead-acid battery is a plate of lead and a plate of lead oxide, with a mixture of water and sulfuric acid between them. Instead of charging and discharging capacitor plates, when you discharge a lead-acid battery you turn the lead into lead sulfate and the lead oxide plate also into lead sulfate, and the sulfuric acid turns into water. Charging the battery reverses this process.
A nickel-cadmium battery has a nickel oxide hydroxide plate and a cadmium plate and an alkaline electrolyte like potassium hydroxide between them. Like the lead-acid battery, it goes through chemical changes as it discharges (the nickel oxide hydroxide plate turns into nickel hydroxide and the cadmium plate turns into cadmium hydroxide) and the reverse happens when it charges. Nickel-metal hydride batteries are similar except that they use an alloy instead of cadmium for the second plate.
As a practical matter, the charge tends to leak off of capacitors, which prevents them from being used as long-term batteries. For short term use (like holding your clock settings while the power goes out for a couple of hours) capacitors have replaced batteries in many applications. Capacitors also charge faster than batteries, and can discharge faster as well.
Inductors also store energy, but they store it in magnetic fields instead of electric fields. A simple inductor is just a coil of wire. In many circuits, an inductor can be used to serve the same purpose as a capacitor and vice-versa. We just tend to use capacitors much more often these days since capacitors are cheaper, smaller, and weigh less.
On preview I see that Chronos ninja’d me a bit, but oh well. 
This is true for simple plate capacitors like the typical ceramic disk capacitor or the tiny chip capacitors that are sprinkled all over circuit boards these days.
When comparing capacitors to batteries, we often use electrolytic capacitors since they can store a lot more energy. While they don’t have chemical changes during charging and discharging like a battery does, the electrolyte (the goo between the plates) doesn’t always age well. A big problem in older electronics is that the electrolytic capacitors often dry out and fail over time.
If you remember the big capacitor problem plaguing the computer industry back in the late 90s up through about 2005 or so, that was caused by some Taiwan companies stealing the formula for the electrolyte and mass producing it more cheaply (yay, profit!). Unfortunately, they didn’t steal the complete formula, and their incorrect formula tended to result in massive capacitor failures after a relatively short time. I had one capacitor blow its top completely off. I heard a pop and then I heard the capacitor case go ping ping ping all around the inside of my computer. Surprisingly, the computer didn’t miss a beat and kept on running. I shut down the computer and opened the case and saw the capacitor case just lying in the bottom of the computer case and thought hmmm, that doesn’t belong there. Didn’t take long to figure out where it came from.
Another similarity between batteries and electrolytic capacitors is that the ‘+’ and ‘-’ ends should generally be attached as directed. I mentioned this in a previous thread.
Then there are Supercapacitors (AKA Electric Double-Layer Capacitors EDLCs), which have higher capacitity but can discharge slowly. As the Wikipedia article notes, they bridge the gap between capacitors and storage batteries.
I’ve replaced the storasge batteries in several hand-crank flashlights with supercapacitors (and have purchased one already built that way). You have to crank up a good charge to use it, but the advantage is that you can leave one sitting in a drawer forever and it won’t be useless when its charge bleeds out, as often happens with rechargeable batteries.
I liken the difference to that between a spring and a bomb. If hypothetically you wanted to shift a heavy object and thus needed a way to release a fair amount of force under it, you could mix together certain chemicals and add a detonator and place your construct (a bomb) under the object. The chemical reactions will release a lot of force in a short time, and the chemicals themselves consumed in the process. You do not need to introduce this force yourself first.
In contrast, picture a large powerful spring. You need to introduce a lot of force to compress this spring, then lock the spring down, put it under the object, and release the lock. It, too, will release a great deal of force in short time, but will not be consumed in the process. You could recover the spring, add a similar amount of force to recompress it, and use it again.
The bomb/battery converts chemical energy to kinetic/electrical energy in a one-time process, while the spring/capacitor only releases whatever kinetic/electrical energy that has been deliberately stored within it and is reusable.
Naturally, this glosses over the issue of rechargeable batteries, but no big deal.
Thats not correct.
The capacitor’s voltage follows an exponential curve that is the solution to the differential equation… as dV/dt = C I(t). This means that they act reactively (differently) to different frequencies, they can be used as components in filters.
The above glosses over a critical difference. (Although I am quite sure most of the above respondents could do a better job of explaining these remaining difference than me.) All the above is talking of capacitors in terms of energy storage. But batteries and capacitors have a number of fundamental differences.
If for battery we mean electro-chemical cell (and ignore the pedantry that a battery is more than one cell) we can first up note that they are polarised. Whilst capacitors used for storage are often polarized (as a result of the construction technique failing if the capacitor is reverse biased) the majority of capacitors are not polarised. Capacitors used for high tension power factor correction and harmonic suppression in power distribution are certainly not of the polarized kind.
But the most important difference is that they behave quite differently in an electrical circuit.
Both devices are characterised by an impedance. However batteries are for all useful purposes purely resistive. Whereas capacitors have, well capacitance, which means a significant imaginary component to the impedance. Capacitors look like an open circuit at DC. A battery looks like a very low resistance. Capacitors pass increasing current as the frequency rises, rising as a linear function of frequency. Batteries still just look like a very low resistance.
Batteries have a terminal voltage that is mostly constant, until depleted. It does not depend upon the stored charge. The terminal voltage of a capacitor is linearly related to the charge it holds.
The impedance (internal resistance) of a battery is dependant upon its state of charge. It is mostly constant through its charge state, but starts to increase as the battery charge is depleted. A capacitor’s impedance is not related to whatever charge it holds, and is constant*.
(Pedantically a battery has an equivalent circuit of a perfect voltage source in series with a resistance. The value of that resistance will vary depending upon the battery’s nature and its state of charge. That variation is also dependant upon the nature of construction, but is not linear.)
The vast majority of capacitors in the world are not used for energy storage but for their reactance.
- Real capacitors of course are not perfect, they have inherent non-linearities, just like any real device versus the theoretical. Capacitors have some resistance and also some (we hope small) inductance. These second order issues effect the precise design of capacitor chosen for an application.
For all the details, see Capacitor Plague.
Thank you to all.
I guess I’m advancing a grade while falling back because of your explanations having given me a little dangerous knowledge, because now I’m moving to a different tack in their definition (exactly as the choices given by Chronos in his very first lesson, post #3):
Again, I’m like a kid in a candy shop here by not hitting the books myself, but as a reader of this book (your posts so far) I understand that, given the inevitable nonlinearities (I’ve come across rise times), each of the little buggers scattered on the circuit board pop as the incoming initiating current enters it (tripwire, sort of).
The frequency of the current in that circuit changes to make the amount of energy in each *pop" release changes at the whim of the designer to change the frequency at that moment in the circuit, to any old level that that capacitor can max out to? And the next go-round of the circuit the frequency may change, so the “passthrough” of that same device (underline above) is different? Or, alternatively, a brother of that same device downstream gets a different frequency and it pops with a different amount?
Wow, I couldn’t parse that at all.
Capacitors act as frequency-dependent resistors. Their “resistance” to AC current is inversely proportional to the frequency. There’s no “popping” going on.
I’m sorry for screwing things up by being verbose–I’ve found in my own teaching of music theory that disentangling a lot of words at the beginning best reveals which to focus on of the truly impressive number of wrong turns the student has made.
Why not use discrete resistors only and just call it a day?
Because using a capacitor allows you do do something useful - make a filter.
Say you want to pass high frequencies, and block low ones. You put a capacitor in series with the signal and a resistor to ground. Since the capacitor has lower resistance at high frequencies, this divider preferentially passes high frequencies (at the rate of 6bd/octave). If you want to block high frequencies, you simple swap the capacitor and the resistor.
ETA: Why would you want to do this? Maybe for a crossover in a speaker, or a tone decoder for a telephone.
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off to fiddle with my floor lamp hand-operated slider to make the light get brighter or softer, and think about it *
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off to look up resistor *
I now have a copy of the text The Resistor Guide associated with this website, which links to its chapters and well represents its style.
I am very happy.
Both a capacitor and an inductor are in fact acting as energy-storage devices when used for their reactance-- They’re just doing it on a very short timescale. At some points in the 60 Hz cycle, a capacitor is storing energy, and at others, it’s releasing it. Likewise for an inductor, except that it’s releasing energy when the capacitor is storing it, and vice-versa. If you have balanced capacitors and inductors in a circuit, then, you constantly have energy sloshing back and forth between them, with no net effect on everything else. If they aren’t balanced, then the effect is in most ways similar to a resistor.
And yes, what the effective resistance (or reactance or impedance) is depends on the frequency. Another place you might want to use a frequency filter is in a radio: When you change your radio from one station to another, you’re still getting bathed in radio waves from both stations (plus whatever other stations are in the vicinity). But your radio is only responding to one of them, because of variable capacitors and inductors that are tuned to only respond to one very narrow band of frequencies.