It is called a solenoid and yes, when the smaller wire has 12volts it energizes the electromagnet in the solenoid, which causes the metal rod inside to move, this does two things, it moves the starter motor gear out to engage ring gear, and it closes electrical contacts that sends the Battery power(larger cable) to the starter motor so it starts to spin.
A solenoid and relay operate the same way, a coil of wire around a metal core, when powered will become an electromagnet.
And the names are often mistakenly used as the same.
For many years Ford had a starter RELAY mounted on the inner fender, but pretty much every one called it the Starter Solenoid.
I got tied of correcting people about it so gave up, same as "Freeze Plugs", lol, they are Core Plugs or Casting Plugs, they plug up holes left in block or heads that were needed to drain the sand out after molten metal casting in a mold.
A RELAY controls power in an electrical circuit, like power window relay
A SOLENOID causes movement, like a power door lock solenoid
With the fender mounted RELAY the battery power was passed to the starter motor from there.
No smaller wire on the starter motor, it was on the fender mounted RELAY, when it got 12volts RELAY closed and starter got power
Last edited by RonD; 07-28-2016 at 08:05 PM.