In Switzerland, we have yogurt with and without sugar, with and without sweeteners, with and without lactose, etc. You can buy 319 different yogurts in the supermarket: https://www.coop.ch/de/search/?text=yogurt

I remember when I lived in the United States, you basically had "fat free" (with lots of sugar) and "greek" (with a little bit of fat, in addition to the sugar). That was 20 years ago, so it might have changed since then.