The timbre is definitely not the same. The electric bass has a long strong granularity and the Jazz electric bass is short and soft. Jazz electric bass has no character, and electric bass has a character, so it was also called the precision bass by the earliest invented user. There are also great differences between character and characterless timbre. You can search for and listen to it on the Internet.
But now many Jazz bands also use Jazz electric bass, but the choice of wood and pickup is different, so the sound is different.
Very rarely used in jazz bands. The Jazz electric bass is much bigger than the guitar and the bass is the double bass. All of us have to stand on the floor and play with a stand on the ground. Otherwise we cannot reach the fingerboard. The bracket stands on the ground to prevent the wear of the body. It can also be used in occasional playing. I believe you will often find it interesting to play the bass in an old jazz band.