shrub vs woody plant

shrub and woody plant both are nouns.

Word	Noun	Adjective	Verb	Adverb
shrub	Yes	No	No	No
woody plant	Yes	No	No	No

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

shrub: a low woody perennial plant usually having several major stems
woody plant: a plant having hard lignified tissues or woody parts especially stems

Other hypernyms of shrub include ligneous plant.

shrub (noun)	woody plant (noun)
a low woody perennial plant usually having several major stems	a plant having hard lignified tissues or woody parts especially stems