costume designer vs costumer

costume designer and costumer both are nouns.

Word	Noun	Adjective	Verb	Adverb
costume designer	Yes	No	No	No
costumer	Yes	No	No	No

As nouns, costume designer and costumer are synonyms defined as:

costume designer and costumer: someone who designs or supplies costumes (as for a play or masquerade)

Other synonyms of costume designer include costumier.

costume designer (noun)	costumer (noun)
someone who designs or supplies costumes (as for a play or masquerade)	someone who designs or supplies costumes (as for a play or masquerade)