This is the yellow or white substance you find on pizzas, sandwiches, with macaroni, in the supermarket, etc. It is produced with one or more real cheeses, which is to say, cheeses that have been made out of milk with a culture of some kind.
The cheese is shredded, melted, and boiled. The melting and boiling kills off anything alive within the cheese, pasteurizing it. Aging is also (obviously) stopped when the cheese is boiled. An emulsifier such as disodium phosphate or tetrasodium tripolyphosphate is then added to make the oil layer rejoin the solid layer. Flavorings and colorings are added, and the resulting "cheese" (which is now only faintly reminiscent actual cheese) is poured into the brick, wedge, or ever-popular loaf shape.
Pasteurized process cheese is regulated by the FDA to contain at most 43% water and at least 47% milkfat.
When nuts, pimentos, chocolate, lint, and/or other random stuff is added, the product officially becomes pasteurized process cheese food. PPCF is regulated for at most 44% moisture and at least 23% milkfat, and additionally, the "cheese ingredient" must account for at least 51% of its weight (which is why cheese hot-dogs aren't PPCFs).
Pasteurized process cheese spread may have a stabilizer like xanthan gum or carrageenan, and must be spreadable at 70 degrees F. Its limits are between 44 and 60% water, and at least 20% milkfat.
If a food doesn't fall within any of these standards, but is still made from at least 51% cheese, it is a pasteurized process cheese product.
A cheese-like substance made from vegetable oil is not a PPC at all, but is instead referred to as an imitation cheese. Mmm, chemicals!
Velveeta is a pasteurized process cheese spread, whereas Velveeta Light is a pasteurized process cheese product. Cheez Whiz is also a pasteurized process cheese spread. Some of the other interesting PPCs available from Philip Morris-owned Kraft Foods, from their industrial food ingredients selection:
Kraft Flavored Cream Cheese in Strawberry and Pimiento flavors
Kraft Pasteurized Process Italian Style Cheese Product
Kraft Pasteurized Process Cheddar Cheese Blend
and my personal favorite,
Kraft Pasteurized Process Hi Melt Old English Cheese
The mouth absolutely waters thinking about them...