four-in-hand vs coach-and-four

four-in-hand and coach-and-four both are nouns.

Word	Noun	Adjective	Verb	Adverb
four-in-hand	Yes	No	No	No
coach-and-four	Yes	No	No	No

As nouns, four-in-hand and coach-and-four are synonyms defined as:

four-in-hand and coach-and-four: a carriage pulled by four horses with one driver

Other synonyms of four-in-hand include coach.

four-in-hand (noun)	coach-and-four (noun)
a carriage pulled by four horses with one driver	a carriage pulled by four horses with one driver
a long necktie that is tied in a slipknot with one end hanging in front of the other