and I do not know what is the generic name for this type of slab. What is it called? I want to use it in the above mentioned design
Typically the long, relatively thin stones (or cast imitation stones) are seen as the tops of walls (though in your first picture the walls may be unseen - in a freezing climate without walls under them the stones will shift every winter) and are called coping stones.
It is possible that in your second picture there is enough porus rock under them to serve as a "railbed" style foundation (there's another term for that which escapes me at the moment - rubble trench?) where well-drained coarse rocks prevent water from building up and freezing to the point of moving the stones on top. I also assume that the visible part of the stones is half or less of the stones overall thickness. Typical coping stones are 2-3 inches (50-75mm) in thickness.
It's also possible that both pictures are from non-freezing climates - perhaps you are as well. In freezing climates, one has to take steps to prevent annual movement from frost.