"Whats in a name?"
Current use of the terms:
Relay = a low amp electric device with an electro-magnetic coil that can close higher amp contacts to pass power.
i.e. a 12volt 40amp relay will close if 12v and ground are supplied to it's coil, less than 1 amp draw to do this, but it's Load contacts are rated for 40amps.
Solenoid = a low amp electric device with an electro-magnetic coil that can move a "plunger" when power is passed thru the coil.
i.e. a 12volt solenoid will cause a mechanical motion to occur if 12v and ground are supplied to it's coil, amp draw varies by how much mechanical power is needed.
But the English word solenoid comes from the French word solénoïde, "the term refers specifically to a long, thin loop of wire, often wrapped around a metallic core, which produces a uniform magnetic field", so an electro-magnetic coil.
So in the beginning and now both a relay and a "solenoid", have a solénoïde inside them, lol.
On the inner fender of older Fords you will find a starter relay, not a starter solenoid, BUT(big but) it is often referred to as a starter solenoid.
Same a Core plugs are called "freeze" plugs, these plugs are used to seal the Core holes from casting a block or heads in a sand mold, nothing to do with freezing.
I assume "back in the day", before anti-freeze, people who forgot to drain their blocks had the water freeze and these plugs were pushed out, so "freeze plugs" became popular name.
It could be argued that the Ford fender mounted starter relay is a solenoid, while it doesn't mechanically "move" anything externally, which is what a solenoid does, it does have a moving "plunger" inside to make the required high amp connections.
Relays generally move an internal contact bar by magnetism without a "plunger" moving.
But it would be a moot point to argue in any case.
Relay makes and breaks electrical connections
Solenoid causes external motion of some mechanical device
A starter motor may or may not have a solenoid attached to it, the solenoid is used to pull/push starter motor's gear into or away from the ring gear, mechanical motion, so a solenoid.
There are other designs like a Bendix Drive, that don't need a solenoid to engage or dis-engage the gears
The newer Ford starters combine starter relay with a solenoid on the starter motor.
These will have a larger post for direct connection to the battery +, so no relay on the inner fender is needed.
And a smaller "S" post for connection to ignition switch, usually via neutral or clutch switch for safety.
So the wiring is fairly straight forward if you know what starter motor you have or will be using.
On vehicles with a starter relay on the fender Ford also used the Battery post on this relay as the alternator hook up and power distribution point, so this relay needs to stay just for the convenience of the existing wiring.
This relay will have a smaller "S" post for the ignition switch wire to activate the relay.
And on the relay's other larger post is a cable to the starter motor, it should be the ONLY cable on this post, this would be for a starter that doesn't have a built in relay, so no small "S" post on it.
If you need or want to switch to a starter motor with built-in relay it is pretty simple.
With new starter motor in place and the larger cable hooked up to it, move that cable's other end from it's lonely large post over to the Battery post on the fender relay, so all the cables and wires should be on that one large post, and starter motor has direct battery power 24/7.
Put the Battery cable on this post first then the starter motor cable, then add the other wires to the post.
Now take the "S" wire off the relay and move it to the "S" post on the New relay on the starter motor, you may need to lengthen this wire.
The fender mounted relay is now just a connection point for power distribution, you can buy insulated posts to replace it, up to you really.