In British English, this would be a shop; an establishment where goods are sold retail. Specifically, it looks like a "corner shop", so called because they are often sited on street corners in residential areas. If you search for images of "corner shop" on Google you will get a lot more examples.
A "store" is the American English equivalent of "shop".
A "market" is a collection of independent stalls within a defined area. In some cases this is within a large open indoor space, and in others it is out of doors. Each stallholder rents a few square yards/meters from the owner of the space, and can then put up tables and awnings and display their goods. The main distinction between "shop" and "stall" is that a shop is permanent whereas a stall is temporary. Again, if you google for images of "market" you will get some good examples.
Note that "supermarket" is not the same as a "market". A supermarket is just a very large shop offering a wide variety of goods. It is not a "market" in the sense described above.