Just a guess, but this is probably done with a strobe and a slow shutter speed. The strobe illuminates for a very short time, so everything appears stop-motion for the duration of the strobe. The rest of the time the shutter is open, much less light comes from the scene, but will have motion blur.
The tricky in this is to balance the continuous lighting and shutter speed to provide the exposure you want for the motion blur part with the contribution from the strobe. The exposure of the strobe-illuminated part is a function of the strobe strength, aperture, and sensitivity. It is NOT a function of the shutter speed or the ambient lighting since that is very weak compared to the strobe when the strobe is on.
Therefore strobe brightness (which includes distance) effects only the strobe component, and ambient lighting and shutter speed only effect the non-strobe parts. By balancing these, you can create effects with the desired mixture of the two. In this case, shutter speed is dictated by how much motion blur you want, so the parameters you get to trade off to balance the fixed and motion-blurred are the strobe brightness and the ambient brightness.