footrace vs fun run

footrace and fun run both are nouns.

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

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

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

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

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