Both words mean "capable of burning". No other real difference. In the US manufacturers are required to use only the word "flammable", but any products already labelled with "inflammable" do not have to be changed. It is really just an instance where the prefix "in" is really out of place. "in" as a prefix has two meanings: 1) 'not' or 'lacking' as in inedible, illegal, implausible, irreverent. 2) 'into, in, on, upon' as with income, intake, implant. Most of the time the difference is fairly clear, but not so with "inflammable".
Thought this was funny: