school bus vs coach

school bus and coach both are nouns.

Word	Noun	Adjective	Verb	Adverb
school bus	Yes	No	No	No
coach	Yes	No	Yes	No

As nouns, coach is a hypernym of school bus; that is, coach is a word with a broader meaning than school bus:

Other hypernyms of school bus include autobus, bus, charabanc, double-decker, jitney, motorbus, motorcoach, omnibus, passenger vehicle.

school bus (noun)	coach (noun)
a bus used to transport children to or from school	a carriage pulled by four horses with one driver
	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

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