wrapper vs jacket

wrapper and jacket both are nouns.

Word	Noun	Adjective	Verb	Adverb
wrapper	Yes	No	No	No
jacket	Yes	No	Yes	No

As nouns, jacket is a hyponym of wrapper; that is, jacket is a word with a more specific, narrower meaning than wrapper:

wrapper: the covering (usually paper or cellophane) in which something is wrapped
jacket: an outer wrapping or casing

Other hyponyms of wrapper include envelope, film, plastic film, gift wrapping, plastic wrap.

wrapper (noun)	jacket (noun)
cloak that is folded or wrapped around a person	a short coat
a loose dressing gown for women	an outer wrapping or casing
the covering (usually paper or cellophane) in which something is wrapped	(dentistry) dental appliance consisting of an artificial crown for a broken or decayed tooth
	the tough metal shell casing for certain kinds of ammunition
	the outer skin of a potato

wrapper (verb)	jacket (verb)
	put a jacket on
	provide with a thermally non-conducting cover