Consider the attwched wiring diagram. The dotted lines represent the bulb/housing. One wire should be attached to each filament and the common should be grounded (left diagram).
If you accidently reversed the ground and turn terminals then when you turned the left turn signal on, one filament on the left would flash and both filaments on the right would flash.
If you only reversed one side, then that turn signal would work correctly.
Given that you say the brightness is different between the sides, I suspect both are wired the same (incorrect) way.
