What is the "circuit opening relay" I do have a relay in the fuse box under the hood.

I'm not saying that the contacts in my starter were not the problem, I just like to know what else it could be? Just in case.

 

It looks to be just the fuel circuit. It it closes when the ignition is turned on.. OK that makes sense. That makes me feel a little better knowing that it probable is the contacts.

 

You are correct. Normally the fuel pump runs when the air flow meter tells it that the motor is running. When you first start the engine, the air flow meter does not have enough flow to trip the fuel pump, so the COR gets it going.