Similarly I think a lot of people learn you get an 11 or 13 by “stacking up” 1 3 5 7 9 11 13 so think you can only call a chord some type of 11th or 13th if you also have the lower extensions present. In practical use, that’s not true. A triad with a 7th and 6/13 can be a type of 13th chord, it doesn’t have to include the 9 and 11 to be called that. One of the simplest 13th voicings is, low to high, C Bb E A - that’s definitely a C13, not C7add13, and definitely not “C13no9no11”!

I see chords like C(add9) all the time and just add a D generally in the higher part of the voicing, above the third, but never add a 7th. C(add2) I might add it lower in the voicing, below the 3rd, but usually pay attention to what’s happening in the melody so I’m not clashing with it. Are you saying (add9) chords are just wrong? Should always be (add2)? If a 9 (or 11, 13) is mentioned without the add bit I assume the 7th is present, as you indicate. I think that’s standard jazz nomenclature

Same for sus2 and 9 chords. If only there is a universal standard for naming chords, and people actually stick to them.

Honest question. Take C E G D where the voice wants to have the D an octave higher(or more) than where it would be if it was spelt C D E G Wouldn’t that not be named as a Cadd9 rather than add 2?

even after music school it took me years to properly understand this LOL

I think a lot of people in this thread aren’t realizing that the primary goal of chord names is to tell you what intervals are in a chord. Not the exact voicing. In some cases it coincidentally is that exact voicing, but that’s usually what the notation below is for. Especially as the chord gets more and more complex.