shut down vs close down

shut down and close down both are verbs.

Word	Noun	Adjective	Verb	Adverb
shut down	No	No	Yes	No
close down	No	No	Yes	No

As verbs, shut down and close down are synonyms defined as:

Other synonyms of shut down include close, close up, fold.

shut down (verb)	close down (verb)
cease to operate or cause to cease operating	cease to operate or cause to cease operating