Old World crayfish vs crawdaddy

Old World crayfish and crawdaddy both are nouns.

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

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

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

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

Old World crayfish (noun)	crawdaddy (noun)
small crayfish of Europe and Asia and western North America	small freshwater decapod crustacean that resembles a lobster