A backfire is actually ignition in the induction side.
That sounds logical (the ignited gasses heading back down the intake), but I never heard of a 'front fire'.
'Backfire' has become the accepted term for fuel / air mixture exploding in the exhaust having passed unburned through the cylinder (because someone turned the ignition off then on, or on closing the throttle on a fast running engine when there's an exhaust air leak). The accepted term for it happening in the carb or intake (the induction side) is 'spitting back'.
Those of us who used to maintain our own (carburated) cars back in the day were very familiar with both as we struggled to get ignition timing and fuel mixture correct.