Old World crayfish vs crawfish

Old World crayfish and crawfish both are nouns.

Word	Noun	Adjective	Verb	Adverb
Old World crayfish	Yes	No	No	No
crawfish	Yes	No	Yes	No

As nouns, crawfish is a hypernym of Old World crayfish; that is, crawfish is a word with a broader meaning than Old World crayfish:

Old World crayfish: small crayfish of Europe and Asia and western North America
crawfish: small freshwater decapod crustacean that resembles a lobster

Other hypernyms of Old World crayfish include crawdad, crawdaddy, crayfish.

Old World crayfish (noun)	crawfish (noun)
small crayfish of Europe and Asia and western North America	large edible marine crustacean having a spiny carapace but lacking the large pincers of true lobsters
	small freshwater decapod crustacean that resembles a lobster
	tiny lobster-like crustaceans usually boiled briefly

Old World crayfish (verb)	crawfish (verb)
	make a retreat from an earlier commitment or activity