Ok, here's the skinny.
Part time locks the front and rear driveshafts together. Basically this gives you '2 wheel' drive...one front, one rear. If you were to put the two right wheels on teflon, they would spin and get you nowhere.
Full Time is a little different, depending on what guts you have in the transfer case. Let's say you have the Selec-Trac from the very first ZJ's with the 4.0. Those were what's called an 'open differential', meaning all 4 wheels are given 25% of the available engine torque, until one wheel slips. Then that one wheel gets 100% torque, and spins, getting you nowhere. This function is nice because it *does* take more to break loose a wheel with 25% than 50% like with rear wheel drive.
The later models with the V8's, etc took it a step further and added what's called a 'viscous clutch' to the transfer case. What this does (when functioning) is sends power "from the wheel that slips to the wheel that grips" ala Subaru, etc. Unfortunately, Chrysler felt it necessary to delete the PT function except for the low range which locks the axles together.
Now, when to use each. Full Time can/should be used all the time. Period. Dry/wet/snowy..whatever.
Part Time can be used when the going gets hairy enough that FT just isn't cutting it, like offroading or snow/ice. It can also be used in heavy rain, despite what others may say. Do *not* however have it engaged on dry pavement, especially when turning. Wanna see aluminum explode?
Hopefully this helps.