blackberry bush vs bramble bush

blackberry bush and bramble bush both are nouns.

Word	Noun	Adjective	Verb	Adverb
blackberry bush	Yes	No	No	No
bramble bush	Yes	No	No	No

As nouns, bramble bush is a hypernym of blackberry bush; that is, bramble bush is a word with a broader meaning than blackberry bush:

blackberry bush: bramble with sweet edible black or dark purple berries that usually do not separate from the receptacle
bramble bush: any prickly shrub of the genus Rubus bearing edible aggregate fruits

blackberry bush (noun)	bramble bush (noun)
bramble with sweet edible black or dark purple berries that usually do not separate from the receptacle	any prickly shrub of the genus Rubus bearing edible aggregate fruits