marriage license vs wedding license

marriage license and wedding license both are nouns.

Word	Noun	Adjective	Verb	Adverb
marriage license	Yes	No	No	No
wedding license	Yes	No	No	No

As nouns, marriage license and wedding license are synonyms defined as:

marriage license and wedding license: a license authorizing two people to marry

Other synonyms of marriage license include marriage licence, wedding licence.

marriage license (noun)	wedding license (noun)
a license authorizing two people to marry	a license authorizing two people to marry