what's the difference- battery pull with charger in
 

There is a reset that is better that a regular battery pull.

You leave the charger in- pull the battery- wait till the red light goes out- insert battery.

What different does this method do as opposed to a regular pull?
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Re: what's the difference- battery pull with charger in
 

I would suggest not leaving the power connected and pulling the battery. You always run the possibility of surging the phone. It may not cause issues in most cases but good electronics practices always suggest power be off during any battery insert.
The LED lite goes out slow due to capacitor discharge.

As for the reboot, the OS reloads in both methods the same.

Re: what's the difference- battery pull with charger in
 

You leave the charger in- pull the battery- wait till the red light goes out- insert battery is to reset the charging history to recalibrate going forward is one reason