Starter motors started off with a FOOT pedal you would push down, that would connect starter motor to battery AND slide the starter gear out to engage the ring gear(flywheel/flexplate)
Moving the starter gear in and out was the big deal to get electric start to work, the electric motor wasn't the big deal, you couldn't leave it engaged(even with no voltage) or it would not work very long, lol
Then a fellow named Vincent Hugo Bendix, invented, AND patented, the Bendix Drive, 1915-1917
It used the torque of the starter motor turning to push out the starter gear but when the ring gear started to turn faster(engine started), the starter gear would retract automatically, so solved the IN/OUT issue
But not everyone want to pay the license fee to use his patents
There were infringements, lol, as there always is on a good idea
But there still needed to be a HIGH AMP "Relay" to activate the starter motor, 60-100amp relay, even with Bendix Drive
The word "solenoid" was commonly used instead of the word relay "back in the day"
Which is why these fender mount relays were often called solenoids, i.e. starter solenoid
A Post on the fender mounted "relay" also became the 12volt power distribution point for the vehicle, or 6volt at the time, the generator was hooked up to it, and any fuses or fusible links or fuse boxes, because it was the Battery's positive post
So that post became an integral part of vehicle wiring, it was still used as a relay, but that one post was used for power distribution
Not everyone want to pay Bendix for his "drive" so they added an actual Solenoid on the starter, it was the bump on top of the starter motor, not a cylinder just a bump
A Solenoid is now defined as an electro-magnetic device that causes movement, so opens and closes a valve, or shifts the position of something, i.e. transmission solenoids, they slide valves in valve body into different positions
A Relay is an electro-magnetic device that opens or close an electrical circuit, i.e. wiper relay or starter relay
So car makers started to add a solenoid on the starter that would push out the starter gear on activation and then pull it back when deactivated, thus avoiding patent fees
After that you saw the Round cylinders on top of starter motors, this was a relay/solenoid combo unit
So ignition switch wire could be run directly to this type of starter by-passing the fender mounted relay completely, but.............
Car makers still had all model vehicles wiring setup to use of the fender mounted relays post as THE power distribution point
So these fender mounted relays were S L O W L Y phased out and were replaced by a "power post" or a larger positive battery cable directly to starter and a small cable directly to engine fuse box
Ignition switch START wire went directly to starter motor relay/solenoid(thru safety switches, lol)
And THEN....................car makers added a smaller starter relay inside the engine fuse box as a Theft prevention add-on
Disables key activation if "alarm" is activated, Ford used it for PATS