I'm from Europe and the industrial butter you find in supermarket is made the same way as american butter. Artisanal butter made by peasants using milk from their own cow is made from the cream that lifts on the top of the container containing milk over a period of 2 weeks, period in which, it ferments.
I didn't knew this. I bought some whipping cream and I whipped it until it became butter and the rests were something similar to this(this is a photo of a lady I found on internet making butter):
The liquid is a tasteless skim milk that is mostly water and milk protein, it is nowhere to be acidic. We refer to this as "zer" from latin: serum. 99% of yogurts found in supermarkets where I live are labeled as "greek recipe yogurt". When you open a greek yogurt, on the top it has a liquid which is also "zer". This one is acidic because of the yogurt underneath, however it is very liquid.
The other that is the true buttermilk used in fired chicken is something we refer as: "lapte acru"(lapte = milk, acru=sour, from latin "acrus"). Which is something, thicker than milk, but thinner than yogurt, which looks like this:
(this is also a googled image)