Tom is correct that usually BS&R items are marked, as least the newer ones. I do have 2 BS&R chef skillets one marked 10 CHEF and the other unmarked. I think that this is a BS&R item, that happens to be unmarked, but maybe Tom P has a marked one to compare too. I don't.
As far as a piece of the market BS&R was a large producer. The first to go to DESI machines, (automated molding machines) and this gave them more capacity than any other cook ware foundry in the US. They had so much capacity that GHC who owned Griswold and Wagner, at one time contacted BS&R to produce their cookware for them. This deal was not completed, and GHC ende up getting their own molding machines. it is hard to go to any flea market in the south and not see a BS&R item, they made that much cast iron.
Now before any one else says it, the newer automated molded items were clunky and heavy, but remember their main goal was to bring the price per unit as low as possible, to compete with cheap imports. Their older items are nicely cast.