Buttermilk is what was left over after having made butter. Either sweet or sour cream was used to make butter. We used to let some milk sit in a crock for a couple of days, unrefrigerated. The cream would settle on top. This cream was skimmed off and accumulated until enough was collected to make butter. It takes about a quart of cream to make about a pound of butter.
We only had one cow and it took several days to accumulate enough cream. Anyway, during the summer and without refrigeration, the cream would have soured but it still made an excellent butter. In the winter the cream was accumulated and because of cool weather, it was still sweet when the butter was churned.
Anyway the cream would be chilled and whipped or beaten until the butter formed. When the butter forms, it is in small pieces in the now buttermilk mixture. The buttermilk was poured off and invariably small pieces of butter went with it.
Buttermilk was considered an excellent drink and also used in many ways in cooking. The butter when separated from the buttermilk would be washed several times and then normally salted and packed into a form for use.
After the cream was skimmed for making butter and the milk was left in the crock to sour. When soured, it was like a single large clump. This clump of soured milk was broken up into smaller clumps. Each clump of soured milk formed a piece of cottage cheese. It was necessary to break up the single large clump but you only wanted to break small enough for the whey to drain. The clumps of soured milk was poured into several layers of cheese cloth and hung up to drip. A clear whey would drip off leaving the cottage cheese.
The longer it was left hanging to drip, the drier the cheese became.