driver's license vs driving license

driver's license and driving license both are nouns.

Word	Noun	Adjective	Verb	Adverb
driver's license	Yes	No	No	No
driving license	Yes	No	No	No

As nouns, driver's license and driving license are synonyms defined as:

driver's license and driving license: a license authorizing the bearer to drive a motor vehicle

Other synonyms of driver's license include driver's licence, driving licence.

driver's license (noun)	driving license (noun)
a license authorizing the bearer to drive a motor vehicle	a license authorizing the bearer to drive a motor vehicle