Well yes that’s true, but they’re all part of the same extended harmony. A jazz musician would see them as the same. The further you delve into extended harmonies the more you realize that every chord is a scale and every scale is a chord (almost. When there’s a major 3rd, we omit the 11th unless it’s #).
So when a jazz musician sees Gmaj7, he sees G, B, D, F#, A, E. And when we add the #11 we can also throw in there the C#.
Now the 5th is commonly omitted since it really gives the least amount of info about the harmony so we don’t need the D. As to the B and F#, well, chances are someone else will play them, or they’ll be part of a melodic figure or something.
Thank You by Zep is a perfect example.
The bass is D, C, G. It’s a very clear I, bVII, IV progression. The little melodic motive that repeats on each chord has the notes E, F#, G.
You can analyze this in a number of ways (and admittedly thinking of the 2nd chord as a C with a #11 is probably not the best way to go. Remember, my earlier post in response to Jeladin was simply answering if if it would sound OK to add a #11 on the bVII). And there really is no perfect way to analyze it that I can think of offhand which is both accurate and reflects the simplicity of it. After reading this thread I’d probably just say “double plagal in D” and then treat the melody as something separate.
If Paige kept the A in there throughout (3rd string, 2nd fret), thus keeping the entire D chord intact and just changing the bass note, it would be easy to write it as D, D7/C (or even just D/C), D/G, and it wouldn’t sound very different. But that would be a lot harder to play on the guitar so the A becomes an open G for the C and G chords.
You can think of it as D, Cadd9, Gmaj7, and this is probably the best way to write it since in the sheet music you have the melody written in. In fact, forget what I said earlier about there being no perfect way. This is the one I think.
But you could also include the melody notes in your harmonic analysis and so the C chord could very well be analyzed as a Cmaj9(#11). The major 7th is missing, but it’s there theoretically, since you know what key/mode you’re in (G/D mixo).