phone message vs message

phone message and message both are nouns.

Word	Noun	Adjective	Verb	Adverb
phone message	Yes	No	No	No
message	Yes	No	Yes	No

As nouns, message is a hypernym of phone message; that is, message is a word with a broader meaning than phone message:

phone message: a message transmitted by telephone
message: a communication (usually brief) that is written or spoken or signaled

phone message (noun)	message (noun)
a message transmitted by telephone	content communicating a message; what something is about
	a communication (usually brief) that is written or spoken or signaled