Generally, language would be considered a subset of communication. However, if you gather two linguists, you will end up with three definitions of language.
It is generally seen as probably the most important distinctive property of human languages compared to other modes of communication that human languages are open-ended, i.e. capable of forming an essentially unlimited set of expressions. This is not the case for any known animal communication system. There have been several other properties proposed as defining for a true language - for example metalinguistics, i.e. the ability to talk about a language in the language itself
Give a man a fish, and you feed him for a day. Teach a man to fish, and he'll invite himself over for dinner. - Calvin Keegan