How do we call cars which 4WD is not always on, however you switch it on using separate gear shift transmission like the picture below.
Thanks in advance.
The type you are showing above is just Four Wheel Drive (4WD). It can be switched between ranges of the transfer case:
With the type you have shown, this is a manual transfer case, shifted by a gear lever. Some older vehicles used to have two shifters sort of in a scissor pattern to do this, whereas now you'll only see one gear shift lever. There is also an automatic transfer case, which has a push button with servos in the transfer case to shift through to the different modes/ranges.
There is also, full-time 4WD, where you can switch between high and low range in the transfer case, but you cannot switch out into a 2WD configuration.
Then there is All Wheel Drive (AWD). This is technically 4WD, but there is only one transfer range, which is always for highway speeds. It is always engaged.