Variations will probably apply, as this sort of thing is rarely "hard-and-fast" in English. This answer is from a US perspective.
Is there a special name for shops where only clothing (also maybe shoes) sold for example Zara or Mango?
I would call this a clothing store. I probably wouldn't call it a shop unless they did a lot of on-site alterations.
There are also department stores. These are named because the store has several departments all under one roof. For example, a typical department store might have:
- a clothing section (where I could by some socks or shoes),
- a furnishings section (where I could buy some drapes or a wall clock),
- a sporting goods section (where I could by a tennis racquet and a dozen golf balls),
- a office supply section (where I could buy a stapler and a ream of paper), and
- an electronics section (where I could by a television and a new case for my iPhone).
There are also chain stores, where you'll find several of same stores as you travel from city to city. This is where the taxonomy gets tricky, though, because several chain stores are department stores, and vice-versa.
More recently, some department stores have added a grocery section; these often get labeled with the prefix super-. So, a Wal-Mart may be a department store, but a Super Wal-Mart (or Wal-Mart Supercenter) is a department store with a full service grocery store in the building.
Chain stores that are not department stores could be classified generically as specialty stores, and more specifically as the kind of store they are (such as grocery stores, sporting goods stores, office supply stores, chain pharmacies, etc.)