hobby vs pastime

hobby and pastime both are nouns.

Word	Noun	Adjective	Verb	Adverb
hobby	Yes	No	No	No
pastime	Yes	No	No	No

As nouns, pastime is a hypernym of hobby; that is, pastime is a word with a broader meaning than hobby:

hobby: an auxiliary activity
pastime: a diversion that occupies one's time and thoughts (usually pleasantly)

Other hypernyms of hobby include interest, pursuit.

hobby (noun)	pastime (noun)
an auxiliary activity	a diversion that occupies one's time and thoughts (usually pleasantly)
small Old World falcon formerly trained and flown at small birds
a child's plaything consisting of an imitation horse mounted on rockers; the child straddles it and pretends to ride