The Jazz bass was introduced in 1960 as a streamlined, ergonomic construction more akin to a Jazzmaster guitar. Like the Precision, Fender nailed it so well the first-time round, they didn’t need to change much for decades.
The offset shape body and back contours are designed with comfort in mind. Hardware-wise, it is fairly similar to the Precision, but obviously depends on the company. The two biggest defining factors are the pickups and the neck.
Most companies that make Jazz shapes equip it with single-coil pickups, making it an extremely versatile bass. You’ll get more treble and middle out of the sound than the P’s lower register. If you’re a fingerstyle or slap player, the Jazz will suit you.
While all newly-built P and J basses have modern ‘C’ shape necks, the Jazz neck tapers off to a slim 38mm nut width. This is unlike the P’s 43mm and consistent size down the whole neck. Ironically, the Jazz will generally offer more precision than a Precision.
Bassists known to play a Jazz include John Paul Jones from Led Zeppelin, Flea from Red Hot Chili Peppers, Noel Redding from The Jimi Hendrix Experience and Rush’s Geddy Lee.