Ah, I mistook "american cheese" with "cheddar". The first isnt cheese, the second one is.
Those american slices in the "cheese"burger, those that come out od the plastic wrapper, we in Switzerland call them "Cheddar" as well.
American cheese often does contain actual cheddar. It's basically a cheese blend that is mixed together with sodium citrate. I live in Germany and American cheese cannot be sold as "cheese" here, the industry usually calls it "Sandwichscheiben", but maybe Switzerland is less strict.
Actually, part of the reason that American cheese cannot be called "cheese" even in the US is that it's not just cheese + sodium citrate anymore. For cost reasons, it's now cheese + butter + skim milk powder + sodium citrate.