First and foremost, there is only one Blues, and that is the "Delta Blues"; all other blues are fakes derived from imitating the "Delta Blues".
When jazz musicians refer to the "Blues", they are referring to the emotion of "Blue" as expressed in their music. Have you ever heard a jazz musician sound like "Howling Wolf"?
The most distinctive aspect of the two Genres (jazz and Blues) is where the artists hone their crafts; the majority of Blues players worked in the deep south originally, while jazz musicians worked the big cities; Chicago, Detroit, LA, and New York. Have you ever heard of a jazz musician playing a "Juke Joint"?
I could go on and on in regard to the differences between not only the differences in musicians, but the differences in music that you can plainly hear, but I wont.