burger vs hamburger

burger and hamburger both are nouns.

Word	Noun	Adjective	Verb	Adverb
burger	Yes	No	No	No
hamburger	Yes	No	No	No

As nouns, burger and hamburger are synonyms defined as:

burger and hamburger: a sandwich consisting of a fried cake of minced beef served on a bun, often with other ingredients

Other synonyms of burger include beefburger.

burger (noun)	hamburger (noun)
a sandwich consisting of a fried cake of minced beef served on a bun, often with other ingredients	beef that has been ground
	a sandwich consisting of a fried cake of minced beef served on a bun, often with other ingredients