beef patty vs hamburger steak

beef patty and hamburger steak both are nouns.

Word	Noun	Adjective	Verb	Adverb
beef patty	Yes	No	No	No
hamburger steak	Yes	No	No	No

As nouns, beef patty and hamburger steak are synonyms defined as:

Other synonyms of beef patty include chop steak, chopped steak, chopsteak.

beef patty (noun)	hamburger steak (noun)
a patty of ground cooked beef	a patty of ground cooked beef