what i'm trying to point out is that the OP's confusion is due to the fact that these are irrational conventions. talking about things like augmented/diminished unisons only serve to increase ambiguity. i have never heard a performing musician refer to unison as anything other than unison (and don't get me started on 'augmented fifths'). something accepted collectively can also be collectively wrong, you know. that is why it's quite relevant to the OP's question.
No, that's not the reason for his confusion at all. It's due to the fact that
he doesn't understand what the existing, well-accepted conventions are. There's nothing particularly irrational about them, and it wouldn't matter all that much if there were, provided that everybody went along with them. A lot of quite useful conventions are quite "irrational," at least by somebody's lights, and so what? English spelling is highly irrational in some areas, yet it represents a convention that is both useful and widely accepted. People have tried to overhaul English spelling in the hope of achieving greater rationality and consistency, and those efforts have all failed utterly, largely because they are answers to questions almost nobody is interested in asking.
I know plenty of musicians, performing and not so much, who know, understand, and can explain what an augmented unison (or an augmented 5th) is and illustrate why and how those terms are used. I'm surprised you don't.
As for something collectively accepted being collectively wrong, that's true in matters of objective fact, like whether the earth is the center of the solar system. But not so much in matters, like this one, where the definition itself is created by collective acceptance. The same idea of "wrong" does not apply. It would be like you telling me it was "wrong" to spell the word "thought" that way, when rationally it should be spelled "thot." You could certainly say that you thought "thot" would be a better and more sensible spelling, but you simply can't say that "thought" is wrong.
What you're saying is not helping the OP understand the difference between a number used to denote the degree of a scale and a number as used to denote an interval between two given notes.