Hi
Not really sure what you are asking here.
What do you mean with "drifting when I have on true airspeed"?
The speed question I understand. It depends on what you want to know.
The speed on the GPS is groundspeed. You could use this to predict if you are going to be late or early. If you are flying into a massive wind your groundspeed will drop (while your airspeed will stay the same). It's a bit like walking on an escalator. If you are walking at 3 miles per hour in the same direction as the escalator's movement you will be travelling pretty fast and you will reach the end of the escalator very quickly. Walk the other way (against the movement) at the same pace and you will hardly move, so it will take you a long time before you're at the end. In the meantime you yourself have been walking at exactly the same speed, 3 miles per hour. You get it?
You're airspeed will always be (just about) the same, depending on what's the best cruising speed for your aircraft.

AJ