I've known some musicians who characterize that kind of playing as lead bass.
One of the best bassists I ever played with loved Phil, Jack Bruce and Casady, and Rick Danko.
The two "best" electric bassists I’ve heard live were John Entwislle (awesome tone) and Jerry Scheff (L.A. studios; Elvis, Roy Orbison, the doors, Dylan, Richard Thompson, Chris Hillman, T Bone Burnett, Elvis Costello). My appreciation of the bass playing of Leland Sklar has been growing greatly in the past few years.