It is no longer produced by mixing existing kinds of cheeses, but by using a number of ingredients. In many countries, including the US, processed cheese is licensed differently to "real" cheese. American cheese may therefore not be sold as "cheese", but as "processed cheese".
On the label, the word cheese is often left out, and the product is labeled "American slices", "slices" or similar. Since this kind of processed cheese is very common in the United States, it is often used to refer to all kinds of processed cheese. All the same, the term "American cheese" does have a legal definition in the American Code of Federal Regulations.