desert rose vs shrub

desert rose and shrub both are nouns.

Word	Noun	Adjective	Verb	Adverb
desert rose	Yes	No	No	No
shrub	Yes	No	No	No

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

desert rose: South African shrub having a swollen succulent stem and bearing showy pink and white flowers after the leaves fall; popular as an ornamental in tropics
shrub: a low woody perennial plant usually having several major stems

Other hypernyms of desert rose include bush.

desert rose (noun)	shrub (noun)
South African shrub having a swollen succulent stem and bearing showy pink and white flowers after the leaves fall; popular as an ornamental in tropics	a low woody perennial plant usually having several major stems