You are referring to the enharmonic note names but there is a difference. The #5 of middle C say is the G# (Ab) in that same octave above middle C.
What you are forgetting is the b13 is the G# (Ab) in the octave above the octave middle C is in. It is a higher note than the #5 you are talking about. Same note but different octave. Jazz voicings refer to these notes eg 9th , 11th 13th etc..They are wanting you to use those extensions in the same octave.
But no reason you have to either. A 9th sits well as a second and some of these notes sound better in a lower octave instead. It just depends on what sounds better. You might a natural fifth for example (G) and putting a #5 right next to it may not sound so good. (G and G# together, some may see this as a clash!) But a G natural in a lower octave and a G# in a higher octave can work and sound quite fine in fact.
Same as singing a bluesy b3 in a higher ocatve while the Maj 3rd is in the dominant chord in a lower octave. All works and sits OK!!