pepper bush vs shrub

pepper bush and shrub both are nouns.

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

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

pepper bush: shrub of eastern and southern coastal United States having beautiful racemes of spice-scented white flowers
shrub: a low woody perennial plant usually having several major stems

Other hypernyms of pepper bush include bush.

pepper bush (noun)	shrub (noun)
shrub of eastern and southern coastal United States having beautiful racemes of spice-scented white flowers	a low woody perennial plant usually having several major stems