An interesting presentation that takes a look at the science of fire extinguishers:

Different fuels create different kinds of fires, and each of these fires need to be extinguished using a very specific method requiring a certain class of extinguisher depending on the type of fire you’re dealing with. Water is often not effective enough because some fires just burn just too hotly to be cooled down by the liquid.

Here are these classes (U.S.):

Need one for your home? This is what you need: A Multi Purpose Dry Chemical Extinguisher.

[SciShow]