cut down vs thin out

cut down and thin out both are verbs.

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

As verbs, thin out is a hyponym of cut down; that is, thin out is a word with a more specific, narrower meaning than cut down:

cut down (verb)	thin out (verb)
cut down on; make a reduction in	make sparse
intercept (a player)	become sparser
cause to come or go down	lessen the strength or flavor of a solution or mixture
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