These two words are nouns of "hamburger", in which burger is short for hamburger.

Supplementary knowledge:

Hamburgers are eaten with cut bread and beef patties, then coated with butter and tomato sauce, and served with various vegetables. They contain a lot of meat and protein and are high in calories. Eating them often or more will make people fat. Hamburgers were also introduced to America from Germany. In Hamburg, German Ports, locals always like to roast chopped beef into beef patties, which are called "hamburger patties". In 1950s, German immigrants brought the cooking skills of hamburger patties to the United States. 1932, some people put this fried beef pie in a bun to eat, and hamburger burger was born. The word Hamburger is spelled very long, and many people like to use hamburger or burger for short.

Typical example:

What do you want, sir? I want a hamburger and some milk. What can I do for you, sir? I want a hamburger and some milk.