heathland vs barren

heathland and barren both are nouns.

Word	Noun	Adjective	Verb	Adverb
heathland	Yes	No	No	No
barren	Yes	Yes	No	No

As nouns, barren is a hypernym of heathland; that is, barren is a word with a broader meaning than heathland:

heathland: a tract of level wasteland; uncultivated land with sandy soil and scrubby vegetation
barren: an uninhabited wilderness that is worthless for cultivation

Other hypernyms of heathland include waste, wasteland.

heathland (noun)	barren (noun)
a tract of level wasteland; uncultivated land with sandy soil and scrubby vegetation	an uninhabited wilderness that is worthless for cultivation

heathland (adjective)	barren (adjective)
	providing no shelter or sustenance
	completely wanting or lacking
	not bearing offspring