ISO Flash and Camera

Reading about inverse square law with flash and ways to compensate flash power. One suggestion is ISO, but it doesn't say on camera or on flash.

So what happens if you have 400 ISO film and Camera set to 400 ISO, if you change the Flash ISO to 800? Or to 200? Obviously the flash power distance will change, more so at 800 less so at 200. But what is the practical effect to changing the flash ISO a separate value than the camera?

This would be fully manual settings, camera and flash.