Tracking speed of the fire control (the component) is a hard limit either way.
Unturreted weapons are also limited to: the higher of ship speed OR Fire Control Speed Rating tech. So if you want unturreted PD weapons on slow ships, that tech becomes a high priority.
Turreted weapons are also limited by the rating of the turret as designed, unless its tracking speed is 0 (in which case it behaves like an unturreted weapon).