Active sensors are much like radar, broadcasting a EM signal which it's built in EM sensor detects as reflections from targets.
The effective tracking speed for turrets is the lower of the turret tracking speed or the fire control tracking speed.
For fixed, non-turret weapons it's more complex. First the weapon tracking speed is the higher of either 4000 the Fire Control Tracking Speed tech or the speed of the ship. Then the effective tracking speed is the lower of weapon or fire control.
Weapons can still hit targets that are faster than their effective tracking speed, just with a reduced chance. Anti-missile missiles can be more effective, but come with ordinance supply and continuing cost considerations. While defensive turrets have a larger initial cost due to needing to have more systems in play.
A common suggestion is to use both with AMM thinning out salvos and turrets cleaning up.