wrapping vs wrapper

wrapping and wrapper both are nouns.

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

As nouns, wrapping and wrapper are synonyms defined as:

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

Other synonyms of wrapping include wrap.

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