[Samsung Galaxy Note 9 Questions & Answers] 6thtry:
Frame rate matters; 240fps (let alone 960fps) might e.g. reveal flickering that is not noticed at 120fps. Each camera could also use different shutter speeds (which is not always the same as 1s/fps). Also, for proper comparison, the compared cameras should be used in the same circumstances (same lamps, etc.)

Quality differences is another topic I'm not going to comment on. There can very well be some, just like with the different quality of photographs with different cameras.

The amount of light does not need to be "extreme", but again, the higher the frame rate, the less time there is to expose (=gather light for) each frame, so the brighter the light needs to be for equal results. Specifically, e.g. 240fps vs. 960fps is 4 times difference in the light needed (if shutter speeds are scaled by the same factor). Or compare normal 30fps to 960 fps, the amount of light might need to be 32 times higher. As an over-simplified example (and not specifically for this Note 9 case), assuming a case where a normal 80W room light would be just enough for a nice 30fps video (shutter speed at maximum to still get 30fps), that light would need to be improved to a whopping 2560W for "equal" exposure with super slow motion. There are other factors affecting it, usually one doesn't really need 2.5kW of light (e.g. I can do a super-slow motion video that only gets a bit on the dark side right at my desk, which has light levels perhaps between recommended "normal room" and "office" levels and corresponds to maybe 20-40W of fluorescent output above the desk - but was it really 960fps, I didn't check), but this discussion is moving towards the territory of general video/photography stuff, other websites are better for these.

The linked video example is obviously made in a studio or studio-like environment, by people who likely know at least a bit on what they are doing ("Slow Mo Guys TV"), so they likely do have appropriately suitable lights (and then some).

The little bit of slowmotion / superslowmotion videos that I have so far taken with Note 9 hasn't shown me anything that I would not have expected (be it flickering lights or result getting too dark etc.) The only things currently in my list of questions related to Note 9 slow motion are: "is the video length in normal slow motion mode limited", "was the very begin and end of one normal slow motion video at normal speed, and if so then why, or does it even matter" and "what was that talk about 480fps and/or 0.2sec snippets I read somewhere (perhaps slips from S9+ or something)".

So, one can always simply try if the slowmotion mode works in the circumstances or not - no need to ignore it in other than certain light conditions - though I would not bother to even try at night, dark street, dim/dark rooms etc. Sometimes the light levels are ok, sometimes they are just too low or the lights are too flickery, in which case one might look for better lighting, and/or move to better lighting (closer to light, daylight outside, another room). Sometimes its tough luck, with no possibility to do decent slow motion video. In some cases one might be able to use certain software to make it slow motion in post-processing (but it has also its own limits). All this is also better explained in photo/video websites.

---------- Post added at 16:45 ---------- Previous post was at 16:25 ----------

To me, the apple basket snippet looked like multiple large diffused lights (or lights with many lamps/sources of light) (and/or reflecting diffusers) from "all" directions (except not from below and less from left); I can't see any shadows there, e.g. the handle only makes slight fuzzy darker area near it, looking like there is at least one light source somewhere up-right.

The dropping water seems to have only one smooth light to left, as reflected from the metal and drop surface, and the drops (when round) do not show anything from behind (or reflections from the front side).

The 3rd scene seems to have at least two not-so-well diffused 4-lamp sources (seen warped in reflections).

But all in all, well arranged lighting in each case (except the bee, where it is likely just the sunlight, no "arrangement" needed).