Also - read the labels on the different coconut milk cans. Some are "lite" coconut milk (= thinner fatty layer and more liquid). If the can does not say "lite" it will be the regular, more fatty coconut milk. (USA stores)
sbhikes mentioned coconut "manna" - I just saw that in my health food store, but I have no experience with that, other than to say that it was in a glass jar, was solid at room temperature, and upon reading the label, has the actual coconut meat in it. Coconut milk is an extract of the coconut meat.