A solenoid is an actuator (it moves something)
In this case it moves the starter gear into engagement with the ring gear on the flywheel.
The relay inside the passenger fender only amplifies an electric switch.
The BL&R (S) wire from the ignition switch makes the relay connect the battery to the starter.
In the case of a PMGR, it is used to trigger the solenoid on the starter itself.
The solenoid on the starter (at least MY 460 PMGR starter) needs 40A to pull and 13A to hold the starter engaged.
I hope this is easy to understand, as we had a question posed yesterday that pointed out Gary's verbiage is not succinct.
Jim,
Lil'Red is a '87 F250 HD, 4.10's, 1356 4x4, Zf-5, 3G, PMGR, Saginaw PS, desmogged with a Holley 80508 and Performer intake.
Too much other stuff to mention.