If the starter solenoid gets stuck, the starter will keep turning, even if you shut the key off. Fords are notorious for that. The contacts in the solenoid get stuck together and create voltage directly to the starter and the only way to shut off the starter is to dis-connect the battery.
If it does it again, tap on the solenoid with a handle of a screwdriver or hammer handle if you can get to it.
When you hit the start switch it closes the contacts in the relay to energize the starter, and when you let off the start switch, it opens the contacts thus shutting off current to the starter.
Looks like you might have to replace the solenoid. I don't think the start switch is to blame, cause if you shut the key off, it should kill the power to it.
I could be wrong, so if anyone else reading this thinks otherwise, please feel free to chime in.