This happens in all supermarkets of Europe, basically. Examples from Germany:
Depending on the store you get either mostly only store products (Aldi, Lidl), both store products and brand products (Kaufland, Rewe?) or mostly brand products (likely Edeka)
The case of what you mentioned is the reason why the Schwarz Group (Lidl and Kaufland) are moving overseas, respectively to the US and to Australia: there isn't much price competition.
Depending on the store you get either mostly only store products (Aldi, Lidl), both store products and brand products (Kaufland, Rewe?) or mostly brand products (likely Edeka)
The case of what you mentioned is the reason why the Schwarz Group (Lidl and Kaufland) are moving overseas, respectively to the US and to Australia: there isn't much price competition.
Disclaimer: work for them.