The phrase "auto tranny" is a slang term used to refer to an automatic transmission in a vehicle. It means that the vehicle does not require the driver to manually shift gears as the transmission automatically does it for them. Full definition
Small truck Good Power Nice auto tranny shifts smoothly Solid classic no frills interior Stock rims looked good and function great Great heater 4wd works well Price, it was thousands less than a Tacoma (autolist.com)
Finally, the 4spd auto tranny is smooth and performs with grace, but seem out of date per current industry standards. (cars.com)
As you mentioned a couple posts ago semi auto trannys are faster but still. (humblemechanic.com)