line of fire vs path

line of fire and path both are nouns.

Word	Noun	Adjective	Verb	Adverb
line of fire	Yes	No	No	No
path	Yes	No	No	No

As nouns, path is a hypernym of line of fire; that is, path is a word with a broader meaning than line of fire:

Other hypernyms of line of fire include itinerary, route.

line of fire (noun)	path (noun)
the path of a missile discharged from a firearm	a course of conduct
	a way especially designed for a particular use
	an established line of travel or access
	a line or route along which something travels or moves