fun run vs footrace

fun run and footrace both are nouns.

Word	Noun	Adjective	Verb	Adverb
fun run	Yes	No	No	No
footrace	Yes	No	No	No

As nouns, footrace is a hypernym of fun run; that is, footrace 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)
footrace: a race run on foot

Other hypernyms of fun run include foot race, run.

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