Close, but not quite.
In the US, there are 5 class ratings for fire extinguishers, A,B,C, D, and K (the classes and their meanings change when you go overseas).
Class A = ordinary combustibles
Class B = Liquids
Class C = Energized electrical equipment
Class D = Metals
Class K = Kitchen fires
Now, when you look at the rating on the side of the extinguisher, it will say something like 10:A,60:B,C. This doesn’t mean that it will put out 10 square feet of ordinary combustibles and 60 square feet of liquids and electrical equipment. The ratings are decided like so:
Class A: The standard unit of “A” is the 2.5 gallon water extinguisher. Each 2.5 gallon water extinguisher is rated as a 2A extinguisher. Since 2.5 gals water is 2.5 gals of water everywhere, it makes a good “standard” unit. The fire that this 2A extinguisher is expected to put out is a certain size and shape wooden crib. If your other-than-water extinguisher puts out this fire, its a 2A. If it puts out 2 of them, its a 4A, and so on.
Class B: Each unit of “B” is the square footage of the surface of the burning liquid. If you have a 60B extinguisher, it will put out 60 square feet of fire on a flammable liquid.
Class C: There is no numerical rating for Class C extinguishers, it only reflects the conductivity of the extinguishing agent. Since your electrical equipment is going to be a Class A or B fire with electricity flowing through/around it, you use the appropriate extinguisher for that hazard plus the C rating so you don’t get shocked.
The number ratings are for a non-trained user of the extinguisher. I know I can put out 400 square feet of burning liquid with a 120BC extinguisher, but I’ve been trained quite a bit in the use of them. The people that use the extinguishers to come up with the ratings are obviously very skilled in their use, so the amount of fire that they can extinguish is down-rated for the average joe.
As for mixing ratings with fires:
In some cases, it can be done without too much harm. In others, you’re going to kill yourself and make the fire larger. Rule of thumb: if you don’t know exactly what the agent is going to do/cause when it hits the material, don’t use it. Can a 2.5 gallon water extinguisher put out a fire in a flammable liquid? Sure can. I don’t suggest anyone try it, but it will work if you know what you’re doing. Stick with the ratings on the extinguisher. You’re also best buying an ABC extinguisher. Can’t really go wrong if you get one.