The balancing current of a typical passive balancing BMS is very tiny. Like milliamps instead of amps. It's often only a resistor for each p-group that can drain any that reach full charge ahead of the others. It turns that extra energy into heat so the bulk charging can continue and the lower voltage p-groups can catch up.
If your battery is poorly balanced, you sometimes have to leave a pack on the charger for days for this process to successfully balance. You can often see the charger blinking on and off regularly while this happens.
A smart BMS will often connect to your phone by Bluetooth and let you see the voltage of each p-group. Some will let you toggle a balancing function on manually that way too, allowing balancing to happen at times other than charging.
If the battery pack is made out of used, old, or poorly matched cells you may want more balancing current to balance faster or more sophisticated balancing methods. Instead of resistors, the p-groups can be connected with a flying capacitor to equalize charge, for example. There are also balancers that can transform voltage, so they can charge any low p-group using a high p-group or the entire pack. When not included as part of a charger or BMS, these can be added as a separate active balancer board. E.g. I have one of these that can transform voltage:
It balances a lot faster than my cell meter which can only drain high p-groups into resistors slowly so as not to make too much heat:
