Jazz and Blues (and now Hip Hop) are the only truly American styles of music. Blues is very simple music that came out of the south based on the blues scale. Chiefly played with a guitar and other assorted instruments. It reflects the life and feelings of the down and out blacks in the poor south. There are several sub-styles - Louisiana Blues, Texas Blues, Chicago Blues to name a few.
More famous artists to check out are Robert Johnson, John Lee Hooker, Buddy Guy, Johnny Copeland, Stevie Ray Vaughn and Eric Clapton.
Jazz has similar roots and also has many styles. Musically it is much more complex than Blues and is more associated with a horn section. Styles include Big Band, Swing, Jam Blues (what everyone thinks is swing), Be-Bop, Cool, etc...
Check out: Duke Ellington, Benny Goodman, Charlie Parker, Acker Bilk, Louie Armstrong, Dizzy Guillespie, Miles Armstrong and very sadly Kenny G.