It's really simple. Use pucks long enough and your CYA (Stabilizer) level will rise so high that you WILL get algae growth--unless you know how to compensate.

Pucks will also drive your pH down so you will always be counter-acting acidity.

Bleach does neither. Bleach adds a little tiny bit of salt to your water, but that just makes it feel softer. It's much easier to calculate how much bleach you need vs how many pucks.

As for the chlorination: there is NO difference once the chlorine hits the water. None, Nada, Gornischt, Rien.