stagecoach vs coach-and-four

stagecoach and coach-and-four both are nouns.

Word	Noun	Adjective	Verb	Adverb
stagecoach	Yes	No	No	No
coach-and-four	Yes	No	No	No

As nouns, coach-and-four is a hypernym of stagecoach; that is, coach-and-four is a word with a broader meaning than stagecoach:

stagecoach: a large coach-and-four formerly used to carry passengers and mail on regular routes between towns
coach-and-four: a carriage pulled by four horses with one driver

Other hypernyms of stagecoach include coach, four-in-hand.

stagecoach (noun)	coach-and-four (noun)
a large coach-and-four formerly used to carry passengers and mail on regular routes between towns	a carriage pulled by four horses with one driver