Valve positioner is responsible for actual accurate positioning of the valve based on PID loop output of 4-20mA DC/0-10 V DC from standalone PID controller or PLC/DCS/BMS loop. It can be electric valve positioner (also called motor positioner) for electric motor actuated control valves or an electropneumatic valve positioner for pneumatic actuated control valves - both accept direct control signal of 4-20 mA or 0 to 10 V DC. This can be a pneumatic valve positioner for a for pneumatic actuated control valve and it would need an extra hardware of current to pneumatic converter (also called I to P converter).
A positioner receives a 0-100% (4-20 mA 24 Vdc) signal from a controller or control system and by measuring the position of the shaft of a valve will add feedback additional force to make the valve go to the chosen position
Position transmitter is the feedback device which gives the valve opening in percentage. This is generally a potentiometer which gives 0 to 1000 ohms or so and at times it is 4-20 mA or 0 to 10 V DC if resistance to current/voltage converter is also integrated.
In simple terms the position transmitter measures the span of travel of any moving object and transmits a 0-100% (4-20 mA 24 Vdc) signal. The position transmitter can be on the shaft of a valve or on the louvers or a cooler, it will transmit the measured distance of movement.