What is the difference between targeted airspeed and selected airspeed?
These terms obviously stem from an Airbus flight deck.

Anything selected represents pilot's discretion. If you want to keep a certain speed, HDG or altitude, you would pull the corresponding FCU (Flight Control Unit = Autopilot Panel) knob. This means in Airbus philosophy: I have control.

Anything managed represents a flight management calculation. If you want to fly, e.g. in the most economic way, you push the corresponding FCU knob and therewith "handover the controls to the aircraft".

The calculations for managed autopilot options are derived from e.g. gross weight entries on the INIT page or current gross weight, Angle of Attack, Air Data Computers, Cost Index, ... depending on the flight phase.

So, you always prefer to follow the economically calculated way and use managed modes. Whenever ATC requests you to keep a certain speed, sink/climb rate, heading whatever, you pull the knobs and select the target values.