spare-time activity vs pastime

spare-time activity and pastime both are nouns.

Word	Noun	Adjective	Verb	Adverb
spare-time activity	Yes	No	No	No
pastime	Yes	No	No	No

As nouns, pastime is a hypernym of spare-time activity; that is, pastime is a word with a broader meaning than spare-time activity:

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

Other hypernyms of spare-time activity include interest, pursuit.

spare-time activity (noun)	pastime (noun)
an auxiliary activity	a diversion that occupies one's time and thoughts (usually pleasantly)