Full Time: The vehicle is always in 4x4, sort of like an all wheel drive system on a Subaru
Part Time: The vehicle is only in 4x4 when you put it in 4x4
Incorrect. Having a part-time 4x4 system like the Wrangler's Command-Trac means simply that it was designed primarily for offroad use and can't be used full time like when on paved streets. A Full-time 4x4 mode like the Cherokee's and Grand Cherokee's Selectrac system has in addition to part-time 4Hi and 4Lo 4x4 modes means it was designed so it can be used all the time, like on paved streets.
For example... the Selectrac 4x4 system available on Cherokees, Grand Cherokees, and Liberties has selectable part-time and selectable full-time modes. It has a 2wd, Full-time 4Hi, Part-time 4Hi, and Part-time 4Lo. You can select any of them, it's not in any particular mode unless you select it.
Part-time means the front and rear axles are mechanically locked together so no differentiation is allowed between the front and rear axles. This type of 4x4 system is designed for off-road use or extremely low traction situations like when paved roads are completely covered with snow or ice. That it is a part-time mode has no bearing on when you use it. The part-time mode term simply means it can't be used full-time since that would also include street use for which a part-time 4x4 system is not compatible.
A full-time 4x4 system places a differential between the front & rear axles so the front & rear axles can rotate at different speeds which makes it usable on paved high-traction surfaces. This is a selectable mode with the Selectrac 4x4 system used on Cherokees, Grand Cherokees, and Liberties. Other brands of vehicles also have selectable full-time 4x4 modes, not just Jeeps.
An AWD system is a full-time 4x4 system that is typically always in 4x4 with no 2wd mode.
Whether a system is part-time or full-time 4x4 has nothing to do with how often it is used. You may have a full-time 4x4 mode in a Jeep Cherokee and never use it, choosing to stay in 2wd all the time. Or it may only be used for that once a year trip up to the mountains... a full-time system that you select with the lever when it is needed for use on paved roads.
Jeep Grand Cherokee WJ - WJ Four-Wheel Drive Systems
Here is a photo of the Selectrac shifter with its selectable full-time and part-time 4x4 modes.