AC power is an alternating sine wave (or some other repeating wave form that hopefully resembles a sine wave to some degree or another). As a waveform, AC has both a frequency and, critically to this discussion, a phase, which in this case refers to how much the voltage component of the waveform either leads or lags the current component. Purely resistive loads don’t affect phase: the voltage component remains in sync with the current component. However, reactive loads (those with either net capacitance or net inductance) affect phase, causing the voltage component to either lead (inductive loads) or lag (capacitive loads) the current component of the waveform. This results in the true power being less than the product of the RMS voltage and the RMS current (which is called “apparent power”), precisely because the two components are out of phase. The difference between true power and apparent power is called “reactive power”, and the ratio between true power and apparent power is the power factor. Power factor is 1 for a purely resistive load and less than 1 for a load having reactive components. For a purely reactive load, which will cause current and voltage to be 90 degrees out of phase with each other, the true power will be zero (regardless of the apparent power) and thus the power factor will also be zero.
The unit of volt-amp (and its multiples) is used when talking about apparent power (the product of voltage and current without accounting for power factor), while the unit of watt (and its multiples) is used when talking about true power. This is largely done to clearly convey whether one is talking about true power (watts) or apparent power (volt-amps). Reactive power is measured in volt-amps-reactive (VAR).
DC, on the other hand, doesn’t have a waveform: it’s just a constant current at a constant voltage, flowing in one direction all the time, not varying periodically the way AC does. As a result DC doesn’t have phase, and so its power factor is always unity; thus, for DC true power and apparent power are always the same and there is no reactive power.
Why does AC use KVA and DC use KW?
Because of an annoying thing called “power factor”.
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