gem vs crown jewel

gem and crown jewel both are nouns.

Word	Noun	Adjective	Verb	Adverb
gem	Yes	No	No	No
crown jewel	Yes	No	No	No

As nouns, crown jewel is a hyponym of gem; that is, crown jewel is a word with a more specific, narrower meaning than gem:

gem: a precious or semiprecious stone incorporated into a piece of jewelry
crown jewel: a precious stone that is a valuable part of a sovereign's regalia

Other hyponyms of gem include solitaire, diamond, ruby, pearl, emerald, sapphire.

gem (noun)	crown jewel (noun)
a precious or semiprecious stone incorporated into a piece of jewelry	a precious stone that is a valuable part of a sovereign's regalia
art highly prized for its beauty or perfection	the most desirable assets of a corporation
a sweet quick bread baked in a cup-shaped pan
a person who is as brilliant and precious as a piece of jewelry
a crystalline rock that can be cut and polished for jewelry