wedding license vs marriage license

wedding license and marriage license both are nouns.

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

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

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

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

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