baby vs babe

baby and babe both are nouns.

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

As nouns, baby and babe are synonyms defined as:

baby and babe: a very young child (birth to 1 year) who has not yet begun to walk or talk

Other synonyms of baby include infant.

baby (noun)	babe (noun)
a project of personal concern to someone	a very young child (birth to 1 year) who has not yet begun to walk or talk
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

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