Are you referring to the AWD system? AdvanceTrac is a stability control system that works through the braking system, not the transfer case. Sport Trac is just an Explorer trim level (the "pickup" conversion).
The older Escapes had Control Trac II, which used a viscous coupler to engage the rear wheels. A manual "lock" would engage a ball ramp and reduce the time needed for the rear wheels to engage. The newer Escapes have the "Intelligent 4WD" system, which replaces that viscous coupling with a computer-controlled clutch. Neither of those use a true transfer case, instead having a PTO mounted to the transmission. It is still referred to as a "transfer case" in some Ford manuals.
Here is what I have on the PTO:
EDIT: That seems to just be the outside...I'll keep looking.