Ist dieser berühmte Käse -Geitost oder Brürest? Gibt es einen Unterschied?

They are different names for the same thing.
There are different types of brunost. Mostly differentiated by the varying content of goat and cow milk. Coat heavy variants are typically darker and have a stronger flavour.

Most commonly known as Brunost. Geitost can be any cheese made from goat milk, so both brown and white cheeses. Brunost can also be made from cow milk, so it’s best to just call it brunost.