Whatjd, don't let all this talk confuse you, it is as you say it is, not as they desire.
Blues people and jazz people are as different as night and day, even when they look alike. First, lets not beat around the bush, blues is defined as "Delta Blues" or some derivative thereof, not as one of those "jazz tunes" with Blues in the title.
The jazz center of the world is New York city, not Jackson or Clarksdale Mississippi.
https://en.wikipedia.org/wiki/Clarksdale,_Mississippi
Most Blues musicians have picked cotton, most jazz musicians have not; that is also a classic cultural difference. I could go on indefinitely, but I wont, I believe you get the picture.