Because when you bridge the posts on the starter, you take power from the mains connection (the large one) and apply it to the solenoid. The solenoid then draws the plunger (extending the pinion) and makes contact with the mains feet to the motor windings. This is also how a "bump switch" works - you clip one lead to the solenoid lead, and the other to a convenient mains lead, and everytime you press the button, you "bump" the engine around a bit with the start motor. If you have the key in and turned ON and hit the "bump" button long enough, you'll start the engine (if you haven't already disabled the ignition.) Likewise, you can turn the engine with the keys in your pocket, using the bump switch.
There may be a "single wire" from the relay to the solenoid, but I don't recall how many connections it may have, nor do I recall what mechanical hazzards may be involved. Also, any time you have wiring "bridging the gap" between the frame/chassis (point of reference) to the engine (relative motion,) you will eventually fatigue the conductors from vibration - I've seen it happen before.
If the starter is tested "on the bench," you have a high-current earth lead, a high-current mains lead, and a low-current solenoid actuation lead. Neither of the leads is HOT until the switch is thrown (typically,) and you can actually do the test with just the high-current mains lead, if you can touch it to both terminals at the same time. Ditto testing a start motor with a set of jumper leads - just clamp the earth lead to the start motor body (usually a mounting ear serves,) and then open the jaws on the HOT mains lead, and touch it to both the starter mains terminal and the small solenoid terminal.
If you remove the solenoid from the starter, you'll see the plunger it uses to draw the pinion gear out, and if you look down the solenoid barrel, you might see the springloaded actuator or actual contacts that close to provide power to the start motor windings.
Make sense now? You'll want to start by backtracing that green wire to the start solenoid, until you find voltage with the key turned to START.
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