Are Targeted Airspeed and selected Airspeed the same thing?
And can someone explain in what cases managed airspeed or pilot selected airspeed would be used, i.e. for different flight phases/situations etc.?
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.
V-Target (should be a subscript Target) is the speed you're going to maintain flying down final in the landing configuration. Your selected airspeed is where you have the cursor right now, so as you go from cruise at say .78 mach to a descent at 280 knots to the descent below 10,000' at 250 knots, to slowing in the pattern to 200 or 210 knots, then configuring with various flap settings, your selected speed changes to each of those, until you've extended the last increment of flaps, and you "set Target" in the window (so that's where your speed cursor goes on the airspeed indicator or tape), and now the Target speed is your selected speed as you fly down final.
You might simplify that explanation to, Target is what you WILL set to fly the final approach in landing configuration, while your Selected speed is what you have selected right now.