Some cosmetic brands are subsidiaries of bigger, more renowned brands (ZA under Shiseido, Bobbi Brown under Estee Lauder & Lancome under L’Oreal etc). If you can’t use stuff from one of the “partner” brands, chances are that you can’t use products from the other “partner” brand as well. This is because the ingredients used in the subsidiaries are usually similar to or are the ingredients used in the parent company’s products.
Similarly, if you are able to use products from the more expensive brand, you’re probably going to be able to use products from the lower-end brand from the same company. This can help you save money in the long run.