Hello and Welcome to the forum.
You are correct, that some transaxles from Toyota have two separate reservoirs for fluid. But in your case, the 2006 Corolla has only a single reservoir for the ATF - you have the correct type - Toyota Type T-IV ATF. Both the transaxle and differential are serviced by the single drain plug on the bottom of the transaxle pan and both refilled via the dipstick. If you got those taken care of already, then you are good to go.