fun run vs foot race

fun run and foot race both are nouns.

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

As nouns, foot race is a hypernym of fun run; that is, foot race is a word with a broader meaning than fun run:

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

Other hypernyms of fun run include footrace, run.

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