heath vs shrub

heath and shrub both are nouns.

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

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

heath: a low evergreen shrub of the family Ericaceae; has small bell-shaped pink or purple flowers
shrub: a low woody perennial plant usually having several major stems

Other hypernyms of heath include bush.

heath (noun)	shrub (noun)
a tract of level wasteland; uncultivated land with sandy soil and scrubby vegetation	a low woody perennial plant usually having several major stems
a low evergreen shrub of the family Ericaceae; has small bell-shaped pink or purple flowers