[computerworks]

This could be an issue of ambiguous terms, but...

I believe the starter system consists of an ignition switch, momentary contact, that energizes a starter relay. The relay allows a low-current switch in the dash to turn on a high-current set of contacts for the starter motor.

When the current is finally applied to the starter motor, a starter solenoid, which is an electric-to-mechanical conversion device, pulls in a clutched gear to engage with the flywheel and crank the engine.

The solenoid engages the starter motor mechanically.
The relay engages the starter motor electrically.

If the starter motor runs on after the ignition switch is released, the relay could be stuck on.
If the starter motor makes an interesting symphony of mechanical noise, the solenoid could not be 'pulling out'