As I understand it.
Lead Pursuit
- where you point your nose ahead of the bandit, attempting to turn tighter and lead for a shot.
Purpose - shoot the bandit.
Pure Pursuit
- where you point your nose right at the bandit, attempting to maintain the same turn and flight path.
Purpose - stay close and tight on the bandit, forcing a mistake by the bandit.
Lag Pursuit
- where you point your nose a bit behind the bandit, attempting follow the bandit, but with less tighter turns than him so as to maintain or even increase maneuvering speed until ready to transition into a Lead Pursuit.
Purpose - stay on the bandit, maintaining speed/maneuverability, while he maneuvers frantically and loses E.