coach vs teacher

coach and teacher both are nouns.

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

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

Other hypernyms of coach include instructor.

coach (noun)	teacher (noun)
a carriage pulled by four horses with one driver	a personified abstraction that teaches
a railcar where passengers ride	a person whose occupation is teaching
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)	teacher (verb)
teach and supervise (someone); act as a trainer or coach (to), as in sports
drive or operate a coach or carriage