The following reference to Baidu encyclopedia--
The name comes from the sixteenth century in the English county of origin Cheddar, is the Somerset County, England, Cheddar local production of a kind of hard full-fat cow's milk cheese, a long history. It has a white or golden color, fine tissue, soft taste and contains 45% milk fat. Today it is widely available in many parts of the world, especially in the United States. It is the second most consumed cheese in the United States (mozzarella being the largest seller), with a per capita consumption of about 4.5 kilograms per year. Because of its high production and consumption in the United States, some people even call it "American cheese". Made from whole milk, it is one of the most basic cheeses, and is also very "all-purpose". It can be substituted for almost any cheese in cooking, from sauces to cheese dressings to baking. Cheddar cheese is very nutritious and contains a lot of calcium.
While cheddar cheese is now produced all over the world, it is only authentic in the British provinces of Somerset, Devon, Dorset and Cornwall. They have a specific trade name, West Country farmhouse Cheddar, and are protected by European Union law (Protected Designation of Origin, PDO).
Yellow Cheddar has a story to tell. Yellow Cheddar, also known as "Mouse Cheese", is the generic name for American Cheese (because Americans love it). It is an unprocessed yellow cheese that has been aged for at least a year. Because the word "mouse" is so unflattering, you'll be hard-pressed to find mouse cheese labeled in supermarkets, but instead you'll find yellow cheddar.
Blue Cheddar is different from regular cheddar in that it is flavored with Blue Cheese. As for the usage, it is not different from the regular cheddar.
Blue Cheddar