baby vs offspring

baby and offspring both are nouns.

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

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

Other hypernyms of baby include issue, progeny.

baby (noun)	offspring (noun)
a project of personal concern to someone	any immature animal
a very young mammal	something that comes into existence as a result
a very young child (birth to 1 year) who has not yet begun to walk or talk	the immediate descendants of a person
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)	offspring (verb)
treat with excessive indulgence