As nouns the difference between crab and cancer is that crab is a crustacean of the infraorder brachyura, having five pairs of legs, the foremost of which are in the form of claws, and a carapace or crab can be the crab apple or wild apple or crab can be the tree species , native of south america or crab can be short for carabiner while cancer is (medicine|oncology|disease) a disease in which the cells of a tissue undergo uncontrolled (and often rapid) proliferation.
As a verb crab is to fish for crabs or crab can be (obsolete) to irritate, make surly or sour.