coat of arms vs arms

coat of arms and arms both are nouns.

Word	Noun	Adjective	Verb	Adverb
coat of arms	Yes	No	No	No
arms	Yes	No	No	No

As nouns, coat of arms and arms are synonyms defined as:

Other synonyms of coat of arms include blazon, blazonry.

coat of arms (noun)	arms (noun)
the official symbols of a family, state, etc.	weapons considered collectively
	the official symbols of a family, state, etc.