"Blues Guitar" I get, but I never quite understood the definition of "Blues Sax".
From JL's list I figure it means R&B and Soul.
No, not at all. Everyone on my list played the blues on a sax. Sure Jr Walker was more of an R&B/soul player, but a lot of that is also blues.
Sax players (and trumpet players, pianists, bassists, etc) have been playing the blues for years, and still do. In fact many electric guitarists learned from those sax players. BB King, for one, cites Louis Jordan as one of his major influences, both vocally and instrumentally (on the sax).
Oh yeah, Louis Jordan should get mentioned here. And also Eddie Cleanhead Vinson. If you don't think Eddie Vinson didn't play the blues, you need to get some new ears.
Also, listen to Charlie Parker on "Funky Blues" or many other blues tunes that he played. That would be one definition of some very sophisticated blues sax, but still right down there in the gutter!
Almost everything Red Prysock and Sil Austin played in their early years was straight ahead 12 bar blues.
And all the jazz guys I listed played plenty of blues that would fit any definition of blues sax you can come up with.
Here's one of my favorite clips of Louis Jordan playing the blues:
There are LOTS more blues sax players, but I'll let others list them.