What year is the starter motor?
Older starter motors just started spinning when they were hooked to the battery, thats how you tested them, they used(needed) a Starter Relay on the fender, often called a starter solenoid(it isn't).
Battery cable was hooked to one large post of starter relay and starter motor was hooked to the other larger post.
The ignition key wire was hooked to the smaller "S" post on the starter relay.
When the "S" post got 12volts from ignition switch it would close the relay and send battery voltage/amps to starter motor.
In later models they moved the starter relay to the starter motor, and made it part of the starter solenoid.
On these you hook starter motor to battery cable via a power distribution post on the fender.
Starter won't spin because starter Relay on the starter motor is not passing battery power to motor.
There is a small "S" post on these that is hooked to ignition switch.
The "S" wire on Fords is usually Red/blue stripe, they used that color for many many years.
"S" wire will only have 12v when key is turn to START, and trans is in PARK/Neutral or clutch pedal is all the way in.
A solenoid is an electrical device that has the purpose of "moving something", on a starter motor it moves the starter gear into or away from the ring gear(flywheel/flexplate)
Pretty much all ford starter motors had solenoids, newer ones also have built-in relay
Some starters only used Bendix drives and didn't used solenoids.
A Relay is an electrical device that has the purpose of "passing power", usually higher amp power.
Solenoids and relays work exactly the same, coil of wire around a movable metal rod, when coil has power flowing thru it the rod moves, and in a relay this will close or open contacts, in a solenoid it will push or pull some lever.
The names are often used interchangeably, as long as you know what you mean it is hair splitting on my part, lol