I think we need to start with "What is cheese?" and then ask what is processed cheese.

Cheese is when you get the protein in milk to clump together and drain the water out. The clump is called a curd. The varieties of cheese come from adding things like salt, bacteria, extra fat, smoke, aging time, etc.

Processed cheese is when you take some real cheese and bulk it up with vegetable gums, milk powder, and other low-cost ingredients. That reduces the price but makes it more bland. It's not much better or worse in terms of nutrition. And crucially, the gum additives make the cheese melt evenly. Most hard cheeses leak oil when they melt. Most soft cheeses are too strongly flavored and too expensive.

The specific Swiss-style singles will depend on whatever that company decides to add in to get the price, flavor, and melt they want. Another company can use a different recipe and call it the same thing.