hamburger roll vs hamburger bun

hamburger roll and hamburger bun both are nouns.

Word	Noun	Adjective	Verb	Adverb
hamburger roll	Yes	No	No	No
hamburger bun	Yes	No	No	No

As nouns, hamburger roll and hamburger bun are synonyms defined as:

hamburger roll and hamburger bun: a round bun shaped to hold a hamburger patty

hamburger roll (noun)	hamburger bun (noun)
a round bun shaped to hold a hamburger patty	a round bun shaped to hold a hamburger patty