Which power is product of voltage and current in a circuit calculated without considering the phase shift that may be present between the voltage and current?

I'm not sure there is a term other than "power"; V*A, or the vector sum of real and reactive power is equivalent to the power calculated by multiplying the voltage times the current, ignoring phase shift.

Answer

The product of voltage and current in an a.c. circuit is called 'apparent power', expressed in volt amperes, in order to distinguish it from 'true power' (in watts) and 'reactive power' (in reactive volt amperes).