get down vs come down

get down and come down both are verbs.

Word	Noun	Adjective	Verb	Adverb
get down	No	No	Yes	No
come down	No	No	Yes	No

As verbs, come down is a hypernym of get down; that is, come down is a word with a broader meaning than get down:

Other hypernyms of get down include descend, fall, go down.

get down (verb)	come down (verb)
take the first step or steps in carrying out an action	get sick
put down in writing; of texts, musical compositions, etc.	be the essential element
pass through the esophagus as part of eating or drinking	criticize or reprimand harshly
lower someone's spirits; make downhearted	move downward and lower, but not necessarily all the way
move something or somebody to a lower position	fall from clouds
alight from (a horse)
lower (one's body) as by kneeling