The Mini/Maxi Rescue Company you mention was actually the Squad Company. They ran back in 70s-early 90s a Tele-Squrt as Squad 1, a pick up w/skid type unit as Squad 2, and a pick up as the 'High Rise Unit' but was Squad 3.
Fast forward to 2011 and beyond, the second piece of the Rescue Co. Is now Squad 1 and runs in place of what Rescue 2 used to respond to which was shootings, stabbings, personal injuries, full or respiratory arrests and could w9rk a Signal 80-MVC w/ a four man 2 piece Engine Company. Rescue 2 now Squad 1 still responds and us still equipped with extrication equipment in the rear bed of the utility body.
The duties for the squad I can't remember I'll check with my sources and get back later
As always stay safe and all go home.
Mini's are 2003-2012 Ford F-350 4x4 3-door or 4-door crew cabs with either Brand FX or Astoria fiberglass bodies there are no longer equipped with water pumps or water tanks but ARE equipped with about 300-500' of 4" LDH to hit a hydrant if need be. They respond to EMS calls solo, the above mentioned calls with the Squad and their Engine on Short telephones, car wrecks and minor fires like pole or vehicle fires. EMS calls leave 2 to staff the Engine for subsequent calks and the OIC and the Mini driver handle the EMS call.