Why are the items on my list grouped by supermarket?

Because it means that while shopping you immediately see what you need in the store you're in — without jumping back and forth between shops. pon assigns each item to the right supermarket and groups the list accordingly. At Walmart, you check off the Walmart section from top to bottom; the things for Kroger sit neatly in their own group.

How does pon know which group an item belongs to? From the item's „Where to buy“ field — estimated at first, then learned from your real purchases. That's why the same item can end up in a different group for you than for someone else: pon goes by your shopping, not by a rigid template.

That way you only need one list for all your stores — and yet, while shopping, only the relevant things are ever together.