British English perspective:
A thermostat is something that keeps temperature constant:
a device that maintains a system at a constant temperature. It often consists of a bimetallic strip that bends as it expands and contracts with temperature, thus breaking and making contact with an electrical power supply
It is therefore something which reacts to the current temperature. Your picture is clearly something which sets what the target temperature is, but I wouldn't (with my limited experience of AC systems) expect it to measure the temperature. (jejorda2 notes in a comment that good AC systems may have temperature sensors in devices like your picture; in which case "thermostat" would be a sensible description.)
A remote control is:
a handheld device that enables remote control of a system or appliance
I would therefore call your picture the "remote control for the thermostat" or possibly "remote control for the air conditioner".
Note that "remote control" in and of itself refers to the device that controls a television. The dictionary link I provided does suggest that this is its only meaning in the US, and it can't be used for a device that controls other appliances. choster, in a comment, suggests that the usage in the US may extend to other appliances.
definitions from Collins Dictionary