Jazz is not Blues and Blues is not Jazz.......

Louis Armstrong, West End Blues.  Define.

Sorry, again with respect, some of you guys are painting with way too broad a brush; or, should I say narrow? Think of it this way:

If “the Blues and Jazz are two completely different genres”, how does one then describe how different the Blues (or Jazz) is compared to, say, European Classical? That they are MORE completely different? THOSE are two completely (!) different genres with entirely different histories, characteristics and aesthetics. The Blues and Jazz are far from “completely” different. The truth is that the Blues is an essential ingredient of Jazz and they share much more than just ethnicity. If you understand the history of each it becomes obvious. To borrow a line used often by someone I know (and you know who you are) “No Blues, no Jazz”.

I’ve always liked food analogies when discussing music. The Blues is to Jazz what Marinara sauce is to Pizza. Way different, right? However, obviously coming from the same place and you can’t have one without the other. Try incorporating tomato sauce in Japanese cuisine; won’t work.  THAT’S completely different. Completely different aesthetics.

Not sure what anyone here means when they say the two get “clumped together“. Is it that Blues tunes sometimes get described as being Jazz; or vice versa? Is it that, for some, discussing one leads to discussing the other; or vice versa? Why not? They are father and child.

Going back to the dawn of recorded jazz and blues in the 20’s there was tremendous cross-fertilization between the genres. They are just sides of a coin, so to speak. 
If one delves into the free jazz genre, the influence of blues is great.  Check out any of Albert Ayler’s recordings to confirm.
Back in the 60’s, it was fashionable to include a slow blues on your average hip jazz album- hundreds of classic Blue Notes followed this formula.

...and fast blues, medium tempo blues and everything in between. Many of those tunes on those Blue Notes are Blues tunes played at faster (Jazzier?) tempos. Good call on Ayler’s recordings. Btw, probably the most prolific and most important Jazz record label, and what did they choose for a name? 😎

For those lacking in technical or historical background, might I suggest one of Ted Gioia’s books. Former Stanford professor of music—and a Jazz musician. He demonstrates the tight linkage between Jazz and blues. And he’s quite readable as an added benefit.