coyote bush vs shrub

coyote bush and shrub both are nouns.

Word	Noun	Adjective	Verb	Adverb
coyote bush	Yes	No	No	No
shrub	Yes	No	No	No

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

coyote bush: widely spreading evergreen shrub of southwestern United States with flower heads in a leafy panicle
shrub: a low woody perennial plant usually having several major stems

Other hypernyms of coyote bush include bush.

coyote bush (noun)	shrub (noun)
widely spreading evergreen shrub of southwestern United States with flower heads in a leafy panicle	a low woody perennial plant usually having several major stems