In this video I saw a photographer (around ~10mins) set up a photograph with a continuous light source; later on the continuous light was switched off, and -to my best guess- the same lighting flashed for the final photo.
Are there strobes which also have a continuous light function?
Studio electronic flash units (strobes) must be properly aimed so that the light plays in an enhancing way on the subject. Because the strobes flash and then quench quickly, aiming is challenging.
Studio strobes have a built-in “modeling lamp”. This is a low-power continuous lamp that mimics how the light from the strobe will play on the subject. It is the “modeling lamp” that you observed.
You are most likely seeing the 'modelling light' which is a feature on lots of studio strobes. It is normally a separate light built close to and in line with the main light in a single unit.
There are a couple of nikon flashes that (sort of) do continuous light for short periods - one of their macro flashes could do very rapidly repeating low power flashes for a few seconds for modelling, basically not actually continuous but fast enough not to be annoying.
And I think some of their speedlights may be able to do some trick (may be a longer than normal discharge ?) so that you can use flash at very high shutter speeds where the shutter only exposes part of the sensor/film at a time (that is, the second shutter curtain follows the first one across, wiping a slot across the sensor, rather than the normal slower flash sync speed where the shutter opens fully, the flash fires, and then the shutter closes). It's sort of continuous, but only for a small fraction of a second. [Edit: having checked some other answers, the on-camera flashes apparently do multiple precisely timed flashes, with feedback from the camera, so that each stripe as the shutter curtains go across gets its own flash - which must be very precise timing to avoid gaps or overlaps, but some studio flashes do the longer discharge I originally mentioned, timing it so the shutter is open during the brightest part].
Neither is really close to the modelling light of a studio strobe.
I'm trying (but failing) to remember whether Nikon ever used a normal torch bulb style light for modelling/focusing in any of their macro flashes - I have a suspicion that they might have done, but I'm not sure. If they did, it was probably in the old macro flash that had the unpluggable high voltage connector lead between the shoe mounted battery pack and the flash head that attached to the lens. (I think the high voltage lead or connector eventually fell foul of some EU health and safety legislation)
