heath vs wasteland

heath and wasteland both are nouns.

Word	Noun	Adjective	Verb	Adverb
heath	Yes	No	No	No
wasteland	Yes	No	No	No

As nouns, wasteland is a hypernym of heath; that is, wasteland is a word with a broader meaning than heath:

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

Other hypernyms of heath include barren, waste.

heath (noun)	wasteland (noun)
a tract of level wasteland; uncultivated land with sandy soil and scrubby vegetation	an uninhabited wilderness that is worthless for cultivation
a low evergreen shrub of the family Ericaceae; has small bell-shaped pink or purple flowers