You'll note that the pickup arrangement is different.
The first one is known as a Precision bass. It has one split pickup. A lot of classic rock sounds in there once you know how to get it out. Sounds absolutely great with flatwound strings on it. Thing classic Motown sound. A lot players swear by them and I love mine. Do a search on youtube for sound samples.
The one you linked to is a jazz bass. It has two pickups--known as single coil pickups. You can adjust the sound to hear one, the other, or a blend of both depending on what you want to hear. Can go from kinda thumpy in the front pickup to really snappy and snarly with the back pickup (known as the bridge pickup.) Fairly common to run both up full since each can hum if used individually. That has to do with the single coil pickups (you'll figure all that out later as you spend more time with the instrument.)
Usually the neck in the Jazz is just a little bit thinner than the neck on a Precision. Neither is right or wrong...they just are what they are. I like both, but you'll likely develop a preference for one or the other.
If you have a store near you, go hold one of each. Slide your hand up and down keeping your thumb no higher than half way up the back of the neck. Decide which is most comfortable and buy the one you want.
Have fun!
