Store brands are genuinely often the same product, just in different packaging. A lot of grocery store labels are actually made by the same manufacturers as the name brands - they're literally using the same facilities and recipes, just without the advertising costs built into the price. For stuff like pasta, canned vegetables, and basic cereals, you're mostly paying for the brand name and marketing when you go premium. The ingredient lists are often nearly identical, and nutritionally there's no real difference.
That said, there are a few categories where it's worth paying attention. Some store brands do cut corners on things like texture, flavor complexity, or ingredient sourcing - you might notice a store-brand mayo tastes flatter, or their yogurt has a different mouthfeel. Oils, spices, and anything with a strong flavor profile can vary more noticeably. And if you care about stuff like organic certification, non-GMO status, or specific sourcing practices, you'll want to read the labels since store brands don't always match what the premium version offers.
The practical move is what you're already doing - try them and see if you notice a real difference. If the store-brand cereal tastes fine to you, there's zero reason to pay more. If something tastes off or doesn't perform the way you want (like if their all-purpose flour bakes differently), then switch back. Most people find they can save 20-30% or so by going store brand on basics without sacrificing anything that matters to them.