The '01 Grand Cherokee Limited came with Quadradrive. This link will explain briefly how it works:
If you search for Quadradrive or 247 transfer case here in the forums, you will find a lot of information on how it works - or not.
The Quadradrive is a hydraulic system. When the rear wheels begin to slip & spin, power is transferred to the front ones. When it works it works really well. But if basic maintenance is not followed, the components fail and it is very expensive to repair.
Your differentials are also hydraulic.
When I bought my '01, I found that the Quadradrive had indeed failed, and it was less expensive to get the mechanical 242 case and a drive shaft from a used parts dealer and have that installed.
I actually prefer that setup because my first Jeep was a '91 Cherokee with the same transfer case. When I pull the lever into 4wd, I know it's fully engaged.
For a few weeks after I bought my '01, I was suspicious of the Quadradrive because it just didn't feel like it was running in 4wd when I needed it to. When winter finally came, I had a really hard time in the snow until I put it in 4Lo. Then it would drive like (better really) than my '91, but you can't really drive too far in Low. Checked the fluid and it was black. Probably never changed by the previous owner. So in went the mechanical case. I've had absolutely no problems since after that.
Got a good local mechanic you trust? drop it off and have the transfer case and differentials tested to see which is working or not.