barren vs heathland

barren and heathland both are nouns.

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

As nouns, heathland is a hyponym of barren; that is, heathland is a word with a more specific, narrower meaning than barren:

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

Other hyponyms of barren include heath.

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

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