Hi
@rja9003. Welcome to the forum! So, the different modes on the Cherokee have been a discussion item for some time because Jeep hasn't really published hard-details on all the system's workings with most of the documents/materials referring to power splits and other high-level details. Even then, there's still not 100% agreement within the Cherokee community on whether it works the way Jeep claims it does. Most information is more based on owner's perceptions.
Most information points to the following:
Snow - with a front wheel biased 60/40 split of torque
Sport - with a rear wheel biased 40/60 split of torque
Sand/Mud - with up to 100% of torque available to the rear axle
Rock - with up to 100% of torque available to the rear axle
As you noted in your post, the most "noticeable" affect of SPORT mode in higher shifting points (which tends to equate to faster take-off), the engagement of the rear wheels (more torque) and disengagement of the traction control. Many use that mode as it provides quicker acceleration than AUTO. It's also very effective when towing because it allows a more powerful take-off from standstill and allows the engine to stay in a higher RPM band when towing a heavy load.
I used to use SPORT mode a lot but now personally use SNOW mode more it has a similar 'power/torque' curve as SPORT but not the so-delayed shifting points which I don't care for.
I don't personally use SAND/MUD mode nor ROCK mode (I don't go off-roading)
Please see the following three items; one's a Jeep video and the other two are threads from this forum posted by forum member,
@Array, that goes into more detail!
Again, Welcome to the Forum!