gator vs crocodilian reptile

gator and crocodilian reptile both are nouns.

Word	Noun	Adjective	Verb	Adverb
gator	Yes	No	No	No
crocodilian reptile	Yes	No	No	No

As nouns, crocodilian reptile is a hypernym of gator; that is, crocodilian reptile is a word with a broader meaning than gator:

gator: either of two amphibious reptiles related to crocodiles but with shorter broader snouts
crocodilian reptile: extant archosaurian reptile

Other hypernyms of gator include crocodilian.

gator (noun)	crocodilian reptile (noun)
either of two amphibious reptiles related to crocodiles but with shorter broader snouts	extant archosaurian reptile