I feel like a "mini-supermarket" is just a market; the super and mini should cancel each other out. :-)
* Convenience Store
* Dollar store (a little more food options at places like Dollar General/Tree/Family Dollar, usually with a small refrigerator section and eggs and milk and juice)
* "Mini" grocery stores, like Piggly Wiggly Express or Dollar General Market
* Stores with mostly food and limited selection like Aldi
* Supermarkets like Kroger and Publix
* Supercenters like Super Walmart and Super Target with full supermarket selection and lots of other stuff