How can I check if the player has moved?

Unity Engine
1

I want a timer to start when the player moves on either x or z. How can I do that with character controller?

2

Cache their starting position, then check if their current position is equal to that starting position.
If not, then the player has moved:

public class Example : MonoBehavior {
   Vector3 startPosition;

   void Awake() {
      startPosition = transform.position;
   }

   void Update() {
      if(transform.position != startPosition) {
         //GameObject has moved.
      }
   }
}