coach vs football coach

coach and football coach both are nouns.

Word	Noun	Adjective	Verb	Adverb
coach	Yes	No	Yes	No
football coach	Yes	No	No	No

As nouns, football coach is a hyponym of coach; that is, football coach is a word with a more specific, narrower meaning than coach:

coach (noun)	football coach (noun)
a carriage pulled by four horses with one driver	a coach of football players
a railcar where passengers ride
a vehicle carrying many passengers; used for public transport
a person who gives private instruction (as in singing, acting, etc.)
(sports) someone in charge of training an athlete or a team

coach (verb)	football coach (verb)
teach and supervise (someone); act as a trainer or coach (to), as in sports
drive or operate a coach or carriage