rain forest vs forest

rain forest and forest both are nouns.

Word	Noun	Adjective	Verb	Adverb
rain forest	Yes	No	No	No
forest	Yes	No	Yes	No

As nouns, forest is a hypernym of rain forest; that is, forest is a word with a broader meaning than rain forest:

Other hypernyms of rain forest include wood, woods.

rain forest (noun)	forest (noun)
a forest with heavy annual rainfall	the trees and other plants in a large densely wooded area
	land that is covered with trees and shrubs

rain forest (verb)	forest (verb)
	establish a forest on previously unforested land