The focus on most discussions of blues and jazz has to do with the similarities -- the common points of origin and the way both genres of music spread up the banks of the Mississippi, both culturally and geographically. The differences between them are both obvious and subtle, with tremendous crossover.
The Delta Origins
The most pronounced difference between blues and jazz is rural versus urban. Although it is difficult to provide precise origins, the spirituals, field hollers and juke joint songs integral to sharecropper culture served as the foundation of the blues, which simplified rhythm, structure and harmony into the musical shorthand of the 12-bar blues form before the end of the 19th century. Jazz, on the other hand, wasn't coined as a term describing music until 1913 in Chicago, although the jazz tradition centered around New Orleans during the same time period.
Contrasting Musical Characteristics
Jazz with its urban origins incorporated elements of European music in both orchestration and theme. Proto-jazz styles of ragtime and Dixieland strayed from both the 12-bar structure and call-and-response lyrics of the blues, giving a more complex and sophisticated cachet to the music. Blues remained a music of the people, with its simple form allowing players of modest ability to participate. Many of the early instruments of blues music were homemade and improvised, while jazz used conventional band instruments.
Instruments and Bands
Jazz bands are larger and soloists more integrated, while blues bands more often feature an artist supported by a rhythm section -- although quartets and big bands exist in both styles. While many instruments are common to both styles, the approach of the players may vary tremendously. For example, jazz drums incorporate sophisticated syncopated rhythms while blues drumming tends toward building a straightforward groove with the bass. Perhaps revealing the rural/urban split, blues favors simple, inexpensive instruments such as the harmonica, while jazz commonly incorporates brass and woodwind instruments such as the trumpet and saxophone.
Melody and Improvisation
Blues melodies and solos generally are built around five-note, pentatonic scales, with bent or slurred blue notes used to invoke emotion. While these are quoted in jazz playing, the pentatonic scale serves only as a starting point for improvisation, free of the restrictive nature of blues form. Traditional Dixieland bands were comprised mostly of single-note instruments such as the trombone and clarinet, leading to the distinctive jazz notion of simultaneous improvisation. Blues bands were built on rhythm sections of drums and bass, with single-note instruments usually improvising alone.
Singing the Message
While both jazz and blues may incorporate singers, blues preserves more of its origins as music of the cotton fields. The stories of hardship and joy in blues songs are integral to the compositions, with the singer bringing emotion and life experience. Jazz vocal styles often highlight the virtuosity of the singer through improvised scat singing, focusing on musicianship more than message.