At least White and Domestic did eventually become the same company, and after that point the Domestics were Whites with a different name - except the ones White made under the Domestic name for Sears, which were basically Singer clones. . .
I have found that most buyers know what they are looking for - so even with a lot of misinformation on the seller's part, the buyer does OK. In fact, I've gotten some super great deals from sellers that didn't really know what they had. And I wasn't going to tell them . . . and ruin my chance at a great deal.