The Stovebolt Site Forums The Shop Area The Electrical Bay Installing led lights in instrument cluster.

A relay is just a switch. In your case you have the original headlight switch and some sort of fog light switch. Either original or aftermarket. Some folks think these switch's contacts/internals can not handle being converted to 12V or handle certain added loads. Therefore they install a relay. A relay is a switch that can handle larger loads. It is operated by the headlight switch and/or the fog switch. It only takes a small current to activate it. The small current powers a small coil which closes the switch. When the switch closes, larger more capable contacts close and finish supplying power to the lamps.
The only thing the headlight or fog light switch does is operate the relay. Your relay is a modern case 30A style. The older horn relays were a tin can style.
Many of the older headlight switches are 30A fuse protected, so it seems they were made to handle the same load as a relay. That is a debate we have had before. They do have big contacts built for 6V currents.
Converting a 6V system to a 12V system does not require a new headlight switch or relays. There is no electrical difference between the 6V and the 12V headlight switch they sell you at vendors.