fisticuffs vs contact sport

fisticuffs and contact sport both are nouns.

Word	Noun	Adjective	Verb	Adverb
fisticuffs	Yes	No	No	No
contact sport	Yes	No	No	No

As nouns, contact sport is a hypernym of fisticuffs; that is, contact sport is a word with a broader meaning than fisticuffs:

fisticuffs: fighting with the fists
contact sport: a sport that necessarily involves body contact between opposing players

fisticuffs (noun)	contact sport (noun)
fighting with the fists	a sport that necessarily involves body contact between opposing players
a fight with bare fists