The UK term for such goods is "own brand", as sold in hypermarkets such as Tesco etc in the UK (and also here in Thailand). They are not normally developed by the store but bulk purchased from the suppliers, who already make similar items, already emblazened with the Tesco etc label.
"Own brands" are typically sold generically, but generic doesn't necessarily mean "own brand".
Before I retired, I used to take proprietary (patented) medication. I now take an equivalent "generic" (patent expired) medication that is an order of magnitude cheaper as the new manufacturers don't have to recoup the huge research and development costs. The generic medication sells under the generic manufacturer's name rather than that of the store that you buy it from, as they have to sell smaller individual quantities through many outlets to make it profitable. It also helps retain their brand image, so you can be confident in buying it at any store in any town where it's available.
own brand - definition of own brand by the Free Online Dictionary, Thesaurus and Encyclopedia.
generic - definition of generic by the Free Online Dictionary, Thesaurus and Encyclopedia.