Actually, the large studs carry the current to run the starter - 125~200 amps - depending on engine, starter etc. The solenoid simply connects the two to make the starter run. I use 2ga. on race cars, but I also use fine strand welding cable, use good parts and make sure everything is in good shape and I'm anal about weight and keeping the cable length to a minimum. I don't have any issues and other folks believe that's too small. 1ga. should be OK, but I wouldn't call it overkill. Some folks will recommend 0, 2/0, or even larger. I would maybe bump it up a size from 2ga. in a street car with some accessories, especially if the battery is in the trunk.

The smaller studs actuate the solenoid. That's a low amp circuit.