Sour mash has, based on my reading of these materials, changed its sense over time, or perhaps always had different meanings. Today, the use of backset in a subsequent mash (fermenter sometimes too) is a hallmark of sour mashing. But one of the 1800's sources I mentioned states that a sweet mash can use backset in this way... This is because sour mash in that account meant essentially dipping back, using the yeast of the last brew to make the next one. That is in a sense the same yeast as when you maintain a culture in a jug but I think too there are important differences due e.g., to much less control on sanitation and temperature. I'll have to look back but if I am not mistaken, this older sense of sour mashing didn't even require the use of backset, but more just the yeast from the former brew. This is one of the methods in that letter from the early 1800's Mike posted which to me sounds like a certain analogy to sourdough bread (but not in the taste aspect). As I now recall, the other method in the letter was called sweet mash and relied simply on use of backset in the next mashing and after that wild yeast did the ferment. I think it is possible that certain local environments favoured the latter process, as occurs with lambic beer in a certain part of Belgium, and this may have been so in Owensboro in the early 1800's. That account based on an interview with Monarch, while there might be an element of puffery in it, can't be made up IMO, it is too specific.