Grocery store is a shop (either convenience, or traditional) wherr we can buy grocery supplies.
The term grocery itself is mostly means any raw or preprocessed food supplies for our daily consumption. The grocery supplies often need to be cooked first. And these what makes grocery store is differ from cafe / restaurants.
Some common example of grocery are vegetables, fruits, milk, cheese, meat, chicken, eggs, spices, etc.
In some countries the grocery is sold in a traditional market where there are several merchant gathered in one place. The market usually established by local gocernment or by the merchant themselves.
In more modern culture, however this kind of market is often replaced by big supermarket / grocery store chain which owned by giant company.
The term of grocery store however is sometimes also used for convenience store which doesn’t sell green groceries.