tree heath vs erica

tree heath and erica both are nouns.

Word	Noun	Adjective	Verb	Adverb
tree heath	Yes	No	No	No
erica	Yes	No	No	No

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

tree heath: evergreen treelike Mediterranean shrub having fragrant white flowers in large terminal panicles and hard woody roots used to make tobacco pipes
erica: any plant of the genus Erica

Other hypernyms of tree heath include true heath.

tree heath (noun)	erica (noun)
evergreen treelike Mediterranean shrub having fragrant white flowers in large terminal panicles and hard woody roots used to make tobacco pipes	any plant of the genus Erica
gaunt Tasmanian evergreen shrubby tree with slender tapering leaves 3 to 5 feet long