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

With respect, I think some of you are missing the point. If you listen to the best Jazz radio stations (WBGO, Newark, NJ for example) they play a great deal of Blues. I’m not sure what exactly the OP means by “some internet sites” being offenders, but Blues and Jazz are intertwined both historically and stylistically; in a way, inseparable and, yes, overlapping. I can’t speak to what “sites” the OP refers to, or whether their motivation is commercial interests, but I can tell you that there are many very musically legitimate reasons for “clumping” them together.

Each to his/her own, and freedom to like whatever one likes.  But like country-rock, "lite-classical,  and other hybrids...some may like and some may not.  As much as I like B.B. King, I do not consider him Jazz and I do not consider Paul Desmond Blues. and I do believe that singers blur that line more often...like Ella and Dinah Washington.  

Have fun, enjoy what you listen to ...even if that is Ernest Tubb. 

I’m actually confused about what exactly the issue is. First it seemed that your objection was to the way some blur the lines when naming the various genres. Not sure how that has anything to do with liking or not liking certain artists or certain genres. Why get hung up with strict definitions? I don’t understand comments like “I don’t consider Paul Desmond blues”. Desmond was a lot of things. He played, at various times, West Coast, Cool, Swing, Ballads and, yes, even Blues sometimes.

According to David Lindley, every song can be made into a reggae song.
I largely disregard genre, other than the short pitch- most music (unless you dig deeply into early ethnic stuff that pre-dates recording technology) has a variety of influences. Genres are for marketing, for ranking (ala Billboard) and radio and its modern equivalents.
To the more specific point, listen to Alice Coltrane’s "Turiya and Ramakrishna" from the Ptah album and tell me that isn’t blues. (Of course, not all blues is jazz or vice versa). But lumping stuff together, making lists and categorizing things is something that humans seem to do, however misleading. It does miss the finer grain details of influences, though. I’ve loved the blues since I was a kid, whether it’s early Delta stuff or later electric blues ala Chicago or elsewhere. Jazz- got tired of the warhorses but a few years ago, my interest was rekindled by so-called "spiritual jazz," "soul jazz" and the output of lots of session players who turned inward after mainstream jazz lost its commercial attraction by the early ’70s. So much music, so little time....

They are definitely different genres but jazz musicians have played the blues since the 40's. Most of what they played was "bop and blues" for decades.  Countless album titles like "Coltrane Plays the Blues" have been made over the years.

Interestingly blues musicians seem much less interested in playing jazz however.