Can someone explain the difference between a Jeep Grand Cherokee 4×2 and a 4×4?

You are correct 4×2 means it ONLY has 2 wheel drive. 4×4 means you can drive in 2 wheel drive on the road and then shift into 4 wheel drive if you have a need to go off road. Hope this helps.

4×2 2 wheel drive only only the rear 2
4×4 2 or 4 wheel drive and yes you can choose the mode rear only or both front and rear
awd all wheel drive and all wheels all the time no choice

the 4×2 jeep grand cherokee will have a solid axle up front(no front differential), no transfer case, and no shift handle for 4×4 operations.
4×4 grand cherokee is exactly that. it is 4 wheel drive and will have a transfer case shift lever.
the full time all wheel drive ( grand cherokee limited v-8 as an example) has no 2 wheel drive
selection available. just high, neutral, and low range. in part time cases you run in 2 wheel drive mode until you need 4 wheel drive. the advantage to this is better fuel economy. in my case i own a 94 grand cherokee limited 4×4 and it is a full time all wheel drive system and the 318 V-8. fuel economy is about 18 mpg for my jeep.

4×2 = only rear wheels turn

4×4 = rear wheels turn most of the time, but you can select to have all 4 wheels turn.

You only use 4 wheel drive when offroad, or in snow. It is not meant to be used on the road.