1985 Jaguar Vanden Plas Starter relay or starter solenoid?

Electrical problem
1985 Jaguar Vanden Plas 6 cyl Two Wheel Drive Automatic

After driving out to check my mail, I turned the ignition key to the off position and without letting the engine die down completely, I goofed and restarted the engine and repositioned the car in my driveway. When I took the key out and exited the car I could hear what I thought was a fan-type sound coming from the passenger side of the hood area. When I opened the hood I found that the starter or something on it was spinning causing the fan sound. I still had the ignition key in my hand, so I disconected the positive cable to the battery and the sound stopped. When I hooked the red cable back to the battery, the engine attempted to start without even having the ignition on. I tried this one more time the starter engaged again, and then I left the cable off and am waiting 'till I find out the solution to the problem. Thank you for your assistance on this, I have an '84 car for parts but I don't know what to swap out to solve this.