As nouns the difference between brie and cheddar

is that brie is a variety of soft, mild French cheese made from cow's milk while cheddar is a cheese styled after the Cheddar cheese made in Cheddar.

As a proper noun Cheddar is

a village in Somerset, England famous for its cheese, and also for its gorge, caves and remains of early man found in them.

As a verb cheddar is

to cut and press cheese so as to remove the whey and leave drier curds.