baby vs cosset

baby is a noun but cosset is not a noun.

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

As verbs, baby and cosset are synonyms defined as:

Other synonyms of baby include cocker, coddle, featherbed, indulge, mollycoddle, pamper, spoil.

baby (noun)	cosset (noun)
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

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