Let's try to get our terminology correct so we can discuss this stuff and know what is being said:
Backfire: A fuel-air explosion occurs in the induction system rather than inside the combustion chamber. Noise, flash, smoke etc. come back out the intake.
Decel Popping (Afterfire): Fuel air mixture that is not completely burned during combustion is ignited in the exhaust system. Noise, flash, smoke etc. come out the tail pipe.
Backfire: A fuel-air explosion occurs in the induction system rather than inside the combustion chamber. Noise, flash, smoke etc. come back out the intake.
Decel Popping (Afterfire): Fuel air mixture that is not completely burned during combustion is ignited in the exhaust system. Noise, flash, smoke etc. come out the tail pipe.