thin out vs cut down

thin out and cut down both are verbs.

Word	Noun	Adjective	Verb	Adverb
thin out	No	No	Yes	No
cut down	No	No	Yes	No

As verbs, cut down is a hypernym of thin out; that is, cut down is a word with a broader meaning than thin out:

Other hypernyms of thin out include bring down, cut, cut back, reduce, trim, trim back, trim down.

thin out (verb)	cut down (verb)
make sparse	cut down on; make a reduction in
become sparser	intercept (a player)
lessen the strength or flavor of a solution or mixture	cause to come or go down
	cut with a blade or mower
	cause to fall by or as if by delivering a blow
	cut with sweeping strokes; as with an ax or machete