Yes aug and alt are two different things I don't thing I said they are the same, but the + is an overloaded symbol. The + can mean Aug, Alt, or sharp a specific note all depending on how the copyist wrote the chord symbol. At same time most will add a b7 to aug chords, and alt will have an altered 5. How and what people do depends on the tune and style its being played in. If I'm doing a pit band and see a Aug or + I'm sticking to the triad. In Jazz or Rock I will probably add the b7 or other color tones, but again have to keep ears open to what's going on. I was always taught Alt or Altered means any combo of altered 5's and 9's. Typically on V in minor but with care can used on any resolving dominant style depending. The b13 is a classic "Juicy Note" in major, you hear Jazz masters resolve it up to the 3rd of a major.