I don't understand the interval thing. Anyone who knows what 'Somewhere Over the Rainbow' sounds like knows what an octave sounds like, and anyone who has seen 'Star Wars' knows a perfect fifth.
Does he mean two notes played at the same time?
Does he mean two notes played at the same time?
Strictly speaking, you can't actually know the name of the interval until you see the written notes, although obviously you can make some educated guesses based on the standard practice of the music style.
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.
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