emerald vs precious stone

emerald and precious stone both are nouns.

Word	Noun	Adjective	Verb	Adverb
emerald	Yes	No	No	No
precious stone	Yes	No	No	No

As nouns, precious stone is a hypernym of emerald; that is, precious stone is a word with a broader meaning than emerald:

emerald: a transparent piece of emerald that has been cut and polished and is valued as a precious gem
precious stone: a precious or semiprecious stone incorporated into a piece of jewelry

Other hypernyms of emerald include gem, jewel.

emerald (noun)	precious stone (noun)
the green color of an emerald	a precious or semiprecious stone incorporated into a piece of jewelry
a transparent piece of emerald that has been cut and polished and is valued as a precious gem
a green transparent form of beryl; highly valued as a gemstone