It depends on the power factor, which depends on the load. Generally speaking, PF is between 0.8 and 1 which means kW is 80-100% kVA. But this isn't always the case; you may be able to calculate it based on nameplate data, but it ultimately will require a measurement to know for sure.

Here is a simple example of the Power Triangle, which will assist with the Power Factor conclusion: (it also doubles as the Basic Impedance Triangle, and the Basic Pythagoris Theorym)

============================================

4 Watts (True Power), 3 VARs (Reactive Power), 5 VAs (Apparent Power).

============================================

Power Factor = 0.8 (80%) lagging 4 Watts is 80% of 5 VA. ---------------------------------------------

Is that supposed to mean the "power" that is scuttling back and forth between the load and the source, that doesn't do any real work, but requires us to upsize conductors and such, in order to accommodate its journey?

I've never heard the term 'scuttle power', but seeing as how it is used as a synonym for reactive power, then 'power going back and forth between source and load' is exactly how I read it.

If you look at a sinusoidal load with a power factor less than 1, you will find that the sine wave representing current is not in phase with the sine wave representing voltage. This means that there will be portions of the AC cycle in which current has one polarity, and voltage the other, meaning that the load is supplying power back to the source. Over the entire AC cycle, the net power delivery is from source to load, but over part of the cycle there is a reverse flow of power.