Salam Alaykum,
Simply seeing a food product with a 'halal stamp' on it does not automatically mean that the product is halal and permissible for Muslim consumption. If you are purchasing from a Muslim supermarket (Muslim owned), you can assume all of their food to be permissible for you, unless you find something out about a specific product they sell.
As for non-Muslim supermarkets - like most of the major grocery chain stores - if the halal stamp on the product has been issued by a known and recognized Muslim organization that certifies halal product and you have trust in them, then you can purhcase and consume that product. Otherwide, if you have doubts, you should ensure you do your own research into that institute and the product before you purchase.