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.
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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.