surname vs last name

surname and last name both are nouns.

Word	Noun	Adjective	Verb	Adverb
surname	Yes	No	No	No
last name	Yes	No	No	No

As nouns, surname and last name are synonyms defined as:

surname and last name: the name used to identify the members of a family (as distinguished from each member's given name)

Other synonyms of surname include cognomen, family name.

surname (noun)	last name (noun)
the name used to identify the members of a family (as distinguished from each member's given name)	the name used to identify the members of a family (as distinguished from each member's given name)