Power/Charger Question

I just finished draining my battery and realzied I need to plug something in to keep using my mac.

So I plugged in the battery charger and my mac is working fine.

So I couldn't help but wonder.....why use the A/C adapter if it runs off the A/C while the battery charger one is in AND charges the battery?

If I understand you correcxtly. The power brick is for running and powering your system. If you are not using your system when and your battery needs charging , then all of the power will go toward charging the battery. If you are using the system at the same time the battery is being charged, then it will take longer for battery to charge.