"Real" current is is a very specific term in electrical engineering, that is that which is in phase with the voltage.
The residential customer is charged only for that portion of the current he draws which is in phase with the voltage.
There is a specific engineering term for the current which is not in phase with the voltage. This current is called "imaginary". Although this current exists and can be measured, the residential customer is not charged for it. "Imaginary" or reactive current does no work, and except for inevitable losses, is returned (reflected) to the power company.
Your ammeter is not aware of phase, so taking a voltage reading and then a current reading gives VA, which is the total of Real and Imaginary power.
A motor will draw power to do work, plus some inductive (imaginary) current which it returns to the power company later. In the simplest case of a pf correcting capacitor, the cap draws imaginary current with the opposite phase from the motor. The goal is that the net outcome is the power company doesn't have any "imaginary" current flowing in and out of the customer premises and therefore is only providing "real" (in phase) current.
You knew all this. Where am I going?
The industrial customer is billed for the real power (work) plus the out of phase (imaginary) current. He often has large inductive loads, and has an incentive to return the power factor to 1 so as to not waste the power company's distribution resources.
The residential customer has a sophisticated meter, but the choice was made for it to monitor only real power (work) and to the best of our knowledge the meters all ignore out of phase (imaginary) current.
A consumer device, however well intentioned, which corrects power factor in the residential environment, can not and does not save any meter clicks.