I have to ask-do you know if they boil the “real” bits of cheese down, and what do they mix it with to make “cheese product”?
While my degrees are in food science, I didn't take any courses which covered cheese making. However, Wikipedia is our friend. I reviewed the 2 Wiki links below, and they do seem spot on.
Milk, water, milkfat, whey, milk protein concentrate, whey protein concentrate, sodium phosphate; contains less than 2% of: salt, calcium phosphate, lactic acid, sorbic acid as a preservative, sodium alginate, sodium citrate, enzymes, apocarotenal (color), annatto (color), and cheese culture.
Processed cheese (also known as prepared cheese, cheese product or cheese singles) is a food product made from a normal cheese (and sometimes other, unfermented, dairy by-product ingredients); plus emulsifiers, saturated vegetable oils, extra salt, food colorings, and/or whey or sugar. As a result, many flavors, colors, and textures of processed cheese exist.
Pasteurized process cheese, which is made from one or more cheeses (excluding certain cheeses such as cream cheese and cottage cheese but including American cheese), and which may contain one or more specified "optional ingredients" (includes both dairy and nondairy items). Moisture not more than 41%; fat in the solids, not less than 49%.
Pasteurized process cheese food, which is made from not less than 51% by final weight of one or more "optional cheese ingredients" (similar to the cheeses available for Pasteurized process cheese), mixed with one or more "optional dairy ingredients" (milk, whey, etc.), and which may contain one or more specified "optional ingredients" (nondairy). Moisture must be <44%, and fat content >23%.