When I design PCBs, I normally come across two specific types of terminal blocks. The images of those terminal blocks are given below.

In the blue terminal block, we can see a small metal strip is pressed down in the slots. In the green terminal block, a small hollow metal box is present which when I screw the terminal, the box comes to the top and holds the wire. What are the actual names of these two types of terminal blocks? In which cases, I should prefer one type over the other?