A general rule is that a defender should always be at least even with the ball, so if your man passes ahead, you have to sprint at least even with the ball and be in the passing lane, between the ball and your man. So, it happens naturally that the D transitions from the full-court to the half-court. It's like a triangle. My coach called it, "ball-you-man". You're always available to slide over and help against penetration and still deny your man the ball by being in the passing lane.
The rest is just coaching decisions. You can trap in different places. You can trap out front on pick and rolls, which I love and we do sometimes. My coach did not generally believe in ball screens offensively because by doing it brought another defender near the ball. We almost always screened away from the ball, setting up cuts. Anyway, thought I'd chime in.