Two or 3 A/C designs....
One: Non Ducted, Controls all in the ceiling panel
Universal replacement, you can put anything you like up there
Two, Diected If you replace the ducting unit.> and it is not also a #3 see above
#3, Remote wall-mounted WIRED thermostat.. Must have the same number of wires (or less) or you will run into problems.
NOTE: Carrier Air V The Wall Mounted "Thermostat" is nothing of the sort and is not wired, It is an I/R remote for the real thermostat which is in the control unit inside the ceiling... if not ducted, See "universal" comment.