Another common denominator between Blues and Jazz is the absolute requirement of being able to "swing". It helps for other musicians, but is absolutely essential for drummers. You might be surprised by how many can’t play a good shuffle (what the swing feel is called in Blues), pure Rock drummers in particular. Not to disparage the dead, but Neil Peart revealed himself as being unable to swing when he performed at the tribute show he put together to honor the recently-deceased Buddy Rich. That’s not me talking Peart fans, that was a number of other pro drummers after the show.
One guitarist who can play both very well is Robben Ford. He was living in San Jose for a while in the early 70's, and I used to see him live regularly (the bassist in my senior year high school band was playing bass in The Charles Ford Band, named after Robben and his two brothers'---also in the band--- dad). Robben later joined Charlie Musselwhite's band, and later Miles Davis himself. Musselwhite and Miles---as Blues and Jazz as you can get, and very different from one another.