The Fender Jazz Bass has a thinner neck, slightly different body shape and contours, and different pickups compared to a Fender Precision Bass. A Fender Precision Bass can be used for jazz just as a Fender Jazz Bass can be used for country, blues, rock, etc. It's as much a player's preference of what bass to play based on what feels best to them as anything else.
The Fender Precision Bass was the first to be introduced circa 1951, and The Fender Jazz Bass came later circa 1960.
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Just a simple question. I often see electric basses, usually Fender, advertised as a jazz bass. I'm just curious. What makes a bass a "jazz" bass? Thanks.