Mark_88, I think you mean the "S" post on starter relay.
"I" post was used years ago to power the Coil when starter motor is active, back then coils only got 7-8volts when engine was running, this prevented early burn out from 13-14volts with engine running.
They used a ballast resistor or resistor wire to lower the voltage going to the coil +
When starter motor was active system voltage is only 10volts so resistor voltage would be down to 4-5volts, too low.
So the "I" wire was used to give coil + the 10volts while starting, "I" post only had voltage when starter motor did.
"S" post/terminal is used to activate the starter relay, on the fender or on the starter motor, which ever you have.
EDIT: oops, reread your post Mark_88, yes "I" post could cause engine not to start, but starter would still crank engine, just no spark from coil.
Yes, the "whats in the name" solenoid-relay debate is always a good one, lol.
And yes the terms were used almost interchangeably for a long time.
The word solenoid actually just references the coil of wire, not any specific use at all.
So relay, ignition coil, PATS antenna and many other things using a coiled wire could be called a solenoid.
Current definitions will usually reference an automotive Relay as a low amp draw device used to activate and deactivate a higher amp circuit.
And a solenoid as a low amp draw device used to cause a linear movement.
A Relay does have that linear movement but that is not the end purpose of a Relay, while with a solenoid the movement is the end purpose, lol, semantics