Let us compare the sound of the "Delta Blues" to the sound of Blues in Jazz;
https://www.youtube.com/watch?v=EyIquE0izAg
https://www.youtube.com/watch?v=s0aIjyX7vwI
Now lets listen to Blues in jazz;
https://www.youtube.com/watch?v=DMgwWAaxQQ4&list=RDDMgwWAaxQQ4&start_radio=1
https://www.youtube.com/watch?v=-488UORrfJ0&list=RDDMgwWAaxQQ4&index=3
All of that music is called "The Blues". Do you hear a major difference between what's called Blues in Jazz and what's called "Blues" since I can remember and even before then? Or is that the difference between "Delta Blues" and all other Blues?
This gets back to the OP's original statement,
Jazz is not Blues and Blues is not Jazz.......