Dollar General has a much larger selection than an Asian 7-Eleven. It has "real groceries" (albeit a small selection) and many non-food goods like detergent, toys, shampoo, even cell phones and a small variety of clothing. It's kind of like they got a list of the top 10% best-selling items at Wal-Mart and made a store out of it.

Dollar Tree (and Family Dollar IIRC) are a bit different because unlike Dollar General each item is actually a dollar. They're a bit more akin to Daiso, if you visited any of those in Thailand, though again with a bit more food (though less than Dollar General, and in smaller packages).