forest vs biome

forest and biome both are nouns.

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

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

forest: land that is covered with trees and shrubs
biome: a major biotic community characterized by the dominant forms of plant life and the prevailing climate

Other hypernyms of forest include dry land, earth, ground, land, solid ground, terra firma.

forest (noun)	biome (noun)
the trees and other plants in a large densely wooded area	a major biotic community characterized by the dominant forms of plant life and the prevailing climate
land that is covered with trees and shrubs

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