neonate vs baby

neonate and baby both are nouns.

Word	Noun	Adjective	Verb	Adverb
neonate	Yes	No	No	No
baby	Yes	No	Yes	No

As nouns, baby is a hypernym of neonate; that is, baby is a word with a broader meaning than neonate:

neonate: a baby from birth to four weeks
baby: a very young child (birth to 1 year) who has not yet begun to walk or talk

Other hypernyms of neonate include babe, infant.

neonate (noun)	baby (noun)
a baby from birth to four weeks	a project of personal concern to someone
	a very young mammal
	a very young child (birth to 1 year) who has not yet begun to walk or talk
	the youngest member of a group (not necessarily young)
	an immature childish person
	an unborn child; a human fetus
	a beloved person; used as terms of endearment

neonate (verb)	baby (verb)
	treat with excessive indulgence