foot race vs fun run

foot race and fun run both are nouns.

Word	Noun	Adjective	Verb	Adverb
foot race	Yes	No	No	No
fun run	Yes	No	No	No

As nouns, fun run is a hyponym of foot race; that is, fun run is a word with a more specific, narrower meaning than foot race:

foot race: a race run on foot
fun run: a footrace run for fun (often including runners who are sponsored for a charity)

Other hyponyms of foot race include funrun, marathon, obstacle race, steeplechase, track event.

foot race (noun)	fun run (noun)
a race run on foot	a footrace run for fun (often including runners who are sponsored for a charity)