wrapper vs wrapping

wrapper and wrapping both are nouns.

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

As nouns, wrapper and wrapping are synonyms defined as:

wrapper and wrapping: the covering (usually paper or cellophane) in which something is wrapped

Other synonyms of wrapper include wrap.

wrapper (noun)	wrapping (noun)
cloak that is folded or wrapped around a person	the covering (usually paper or cellophane) in which something is wrapped
a loose dressing gown for women	an enveloping bandage
the covering (usually paper or cellophane) in which something is wrapped