How is it that bleach seems to remove colors from almost anything, even a black color, virtually regardless of the source of the discoloration? Let’s begin with explaining what is bleach, chemically. Obviously, it is some Cl compound in an aqueous solution. But, then again, so is ammonia, so what’s so special about bleach? - Jinx
Ammonia does not contain chlorine. It’s formula is NH[sub]3[/sub].
And bleach is not always a chlorine compound. It’s not the chlorine in bleaches that does the work, it’s the oxygen. Bleaches are oxidizers. Hydrogen peroxide, for example, contains no chlorine, but it is an effective bleaching agent. The reason bleaches make colors fade or disappear entirely is because of the oxidizing action. It breaks down pigment molecules into various oxides which can no longer absorb and emit light to appear colored and often are simply dissolved into the water around them.
When you say “oxidizers”, do you mean as in the sense of “oxidation-reduction”, or that they have an affinity for O2? (The way chemists use that verb “to oxidize” has never sat right with me!) - Jinx
This one. That is to say, bleach causes stuff to oxidize in its presence.
I’d like to mention that it doesn’t just break down pigment molecules. In fact, bleach is the fundamental reason why I, at age 12, took over household laundry duties from my mother. She ruined my favorite pair of white jeans by pouring straight bleach on the grass-stained knees. What came out of the washer was shreds of white denim. That was the end of my mother’s reign as family laundress.
I am a laundry goddess. :rolleyes:
Spray 'n Wash Dual something (double chambered thingamabob) is the best stain remover out there. The stuff is amazing. I find bleach yellowing yet I use it, in small quantities, for disinfection of items like sheets and towels.
I’m really more of a laundry muse. 
A general understanding of where the color comes from would help. Most of the stains you are dealing with will be composed of organic pigments. Organic pigments get there color from the arrangement of pi-bonds (usually double bonds) that results in an interaction that lowers the energy difference between the highest occupied molecular orbital and the lowest occupied molecular orbital.
That sounds complicated, but it isn’t that bad. The point is that a single pi-bond is not enough to lower the energy to interact with visible light. A series of pi-bonds in a row, however can interact to make the energy low enough to be in the visible spectrum.
Sodium Hypochlorite (bleach) reacts with pi-bonds. This breaks up the series of overlaping orbitals into smaller bits making the organic pigment colorless.
Blood of course is one where the color is resulting from transition metals. When bleach is used on blood stains, it works by making the iron water soluble so that it can be washed away. At least that is how I reason it out because oxidizing the iron will not make it colorless.
Bleach is sodium hypochlorite (NaOCl). Ammonia is ammonium hydroxide (NH[sub]3[/sub]) so not a chloride compound, but perhaps you were thinking of table salt (NaCl). What is important about bleach is the oxidation state of the chlorine atom. In sodium hypochlorite the chlorine is in the oxidation state of +1. In sodium chloride, the oxidation state is -1. Chlorine is not happy in the oxidation state of +1, so it will readily steal electrons from anything that will let it. Chlorine in the -1 oxidation state has a full octet of electrons so is perfectly happy on its own.
When something bonds with oxygen, it is said to be giving up it’s electrons to oxygen. In that sense, the two definitions you propose are identical.