"push-button" refers to how the 4WD system is engaged vs. a simple lever on the floor/console (usually with 2Hi-4Hi-N-4Lo positins). All truck-based 4x4's have a transfer case, which is located behind the main transmission and splits the drive power to the front and rear axles. Car-based SUV's have a transfer case as well, but it's typically integrated into the main transmission.
SUV's with AWD generally won't have any lever or buttons for the 4WD mechanism - it's generally controlled by a computer. Additionally, I've never heard of an AWD system that had a Lo range. Sometimes, there will be a "4-lock" button that will lock the transfer case so that power is always equally split to both axles.
I think Cherokee's were available in either 4WD or AWD trim. If there's no buttons or lever for the 4WD, then it's AWD.

