I’d argue that the “indistinguishable” term was carefully, and wisely, selected by Clarke. He knew what he meant and he meant what he said.
IMO …
The key thing about true magic, the kind the Ancients believed in, is that the [whatever] simply occured when bidden by the wizard or invisible god. There was absolutely nothing in the experience of the witness that gave the slightest purchase on how. The how was unthinkably inaccessible, belonging to a completely different universe of experience and expectations. The wizard having just conjured up a rabbit, might was well next fly, or disappear, or create a giant chasm in the floor spewing butterflies or demons. Or both.
The mind of the observer has no purchase on the observation beyond simply having recorded what they saw like a bit of film; comprehension or analysis is over before it begins. Dead end, full stop.
That was then. What about now? If Clarke had written in 1000AD we could argue that maybe we’ve come far enough his thoughts are invalidated. He was writing in 1962. I was 5. Humanity has not come very far in that time, although some of our tech has gone aways.
If I saw a spaceship the general size & conformation of an imperial Star Destroyer simply appear overhead, that’s magic. I cannot extrapolate from current science or current engineering to how they did that. Yes, it’s a familiar trope from fiction. Fiction that never explains, except with technobabble, how it works.
I can accept, here in 2022, that some other society on some other planet does know how to do that stuff. So a scientific explanation is possible in principal. But Clarke and even age 5 me in 1962 knew that already then. The difference of 60 years changes nothing. It’s not possible to even start to explain with Earth 2022 science.
Try this: Any sufficiently advanced technology is so far advanced from your own that there is nothing about the new stuff that you can extrapolate from any of your current stuff; it’s simply a bridge too far, a blind leap into the unknown with no landmarks to help you. At which point it may as well be magic for all the ability to figure it out you (don’t) have. IOW, it’s indistinguishable from magic.
Observing any one conjuring, (e.g. the Star Destroyer) tells you bupkiss about what else they might be able to do.