[superpope99]

I believe what he is referring to is the idea that you can't tell the difference between eg. an "augmented second" and a "minor third". One is written e.g. C-D#, one C-Eb. I've always found the distinction between these two types of interval largely pointless - for exactly his reasoning. They sound the same.

Potentially they are useful in discussing theory in writing, potentially they are relevant when tuning using non-equal temperament. But knowing this distinction doesn't help you make music that sounds good. An ear trained pianist, for example, would not distinguish these two intervals, and I would argue that would not be a limiting factor to the quality of music they could produce.

[HPsquared]

It depends on the instrument and tuning system. In 12-tone equal temperament they are the same. Some tuning systems treat them differently though, in fact some early keyboards had separate keys, the black keys were split in two so D# was a different key to Eb. Called "split sharps".

https://en.m.wikipedia.org/wiki/Split_sharp

[21echoes]

the reason they are named differently and are notated differently is that they serve different functions. they're more or less homophones.

or, perhaps to keep it within the artistic sphere, they're like https://en.wikipedia.org/wiki/Checker_shadow_illusion and other "same color" illusions -- they are technically the same, but taken in context they signify different things.

you would build different chords around them, you would play different melodies around them, etc. in other words, it's not just when writing them out in english that we treat those two intervals differently -- we treat them differently while using them during music

you are, of course, correct that many very competent musicians would not correctly name this distinction using the official theory terms. but that doesn't mean that they don't understand the distinction when using them in musical contexts, or that the distinction is not meaningful. plenty of professionals are experts at something without being able to describe it perfectly in words