lavender cotton vs shrub

lavender cotton and shrub both are nouns.

Word	Noun	Adjective	Verb	Adverb
lavender cotton	Yes	No	No	No
shrub	Yes	No	No	No

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

lavender cotton: branching aromatic Mediterranean shrub with woolly stems and leaves and yellow flowers
shrub: a low woody perennial plant usually having several major stems

Other hypernyms of lavender cotton include bush.

lavender cotton (noun)	shrub (noun)
branching aromatic Mediterranean shrub with woolly stems and leaves and yellow flowers	a low woody perennial plant usually having several major stems