tug-of-war vs athletic contest

tug-of-war and athletic contest both are nouns.

Word	Noun	Adjective	Verb	Adverb
tug-of-war	Yes	No	No	No
athletic contest	Yes	No	No	No

As nouns, athletic contest is a hypernym of tug-of-war; that is, athletic contest is a word with a broader meaning than tug-of-war:

tug-of-war: a contest in which teams pull of opposite ends of a rope; the team dragged across a central line loses
athletic contest: a contest between athletes

Other hypernyms of tug-of-war include athletic competition, athletics.

tug-of-war (noun)	athletic contest (noun)
any hard struggle between equally matched groups	a contest between athletes
a contest in which teams pull of opposite ends of a rope; the team dragged across a central line loses