Used to be called "samousluga" (self-service), and everyone knows the word, and everyone will refer to them as such, it's just that the odds of seeing the word above any door is practically nill. It's all now a market or supermarket or diskont or something of the sort.
There are various kinds of these, from little mom'n'pop shops on the corner, sometimes claustrophobically small, to your regular corner market, sized approximately as a 7-eleven or a larger gas station shop, up to megamarkets (yep, those too) which may be as large as a supermarket area of a typical Walmart.
The assortment of things you can buy in a samousluga has changed over the years. Nowadays they also carry trustworthy vegetables and fruit; once upon a time you had to be in a real hurry to buy there, because nobody trusted the stuff bought in the shop - for those, you went to the green market. Also, bread now comes in paper bags, whereas it used to be routinely transferred by hand from the plastic crates, straight off the truck (just like a small U-haul but with shelves, filled with those crates), and laid open on the shelves. The rest of the stuff is generally the same as anywhere else; anything you may need in a kitchen, bathroom or yard (though not the garden tools etc), and some of barbecue stuff - charcoal, tongs, skewers.
What's new - the same kind of lower-end small appliances (blowdryers, toasters and such), which nobody sane would have bought in a samousluga - that was hardware store stuff - now are the same cheap Chinese plastic jobs just like anywhere else. But that's only in the really big ones; in a medium sized ones, don't expect anything technically more complicated than a mop.