Drones use both a receiver and a flight controller. The flight controller receives the receiver input and outputs signals to the motors to move the drone in a direction reflective of the user input.
Fixed wing aircraft typically only use a receiver. The receiver takes user input from the transmitter and outputs signals to the servos or speed controller/motor on the aircraft. Some fixed wing aircraft also use flight controllers similar to drones. They receive the receiver input and either pass it through to the servos/motor, or alter it in some way to provide auto-levelling capabilities, GPS guided flight, and more.