What makes the same model of a bass sound different?

Different piece(s) of wood, different sound. How the neck and body couple. Innumerable variables. When you are dealing with organic substances like wood, you have to expect variations on the theme.

 

Different things are different, and, sometimes similar things are different, too.

Thus, is variety made.
Embrace it and enjoy the ride.

 

I think the strings and setup have more to do with it than anything else. I know I play differently on basses that are set up differently, unconsciously. I know too that a brand spankin new set of strings on an untouched bass will make that bass sound completely different than one that's been hanging on a rack in a GC for even a week.

Wood I'm sure adds to the difference... but I honestly think that difference is negligible on same model basses.

And I'm also half deaf, so maybe I just don't notice anymore .

 

Fo reelz, imo it's a combination of elements, from the actual hardware components, to variables like wood density and stiffness, glues, finishes, and attention to details like properly tightening all screws, and preparing the neck/body joint.
I'm looking at a new-ish P bass, and there are 28 screws in the body, and 21 in the neck, all fastening different things, and the variance in any could vary all. Rattles, looseness, etc. Add the above, etc, and the deficiencies can mount up quickly. There's a lot of small errors possible.

The big things are all little things.

 

At one point in the game I owned six Jazz Basses in the same finish (sunburst/rosewood) ranging from '68 to '74 and every single one of them had its own personality. So yes, regardless of whatever one decides to attribute the differences in sonic proportions to, they very well may exist even amongst the most similarly looking instruments made by the same manufacturer.

More recently, when I was buying my Les Paul Special (guitar, not bass) I tried four of them along with the one that went home with me. The differences might have been subtle, but they most certainly were audible to me.

Stuff like this is to be expected, IMO, for most guitars and basses.

 

Strings, setup, pickup height, wood, even finish.
We can talk all day about generalities of what does what and how much,
but in the end it comes down to the combined effects of everything involved.
Further, it's hard to say what is best because what is best for me might be
very different from what is best for you.

 

There's Yer problem! (southern accent). You bought it online. I never purchase instruments online. I must play an instrument before I purchase. Just my OCD.

 

It can also depend on what day of the week it was made/put together. Mondays and Fridays being being hit or miss?

 

It's a combination of how you hold your mouth when you play, and stray cosmic rays....
Seriously, though; post #7 pretty much nailed it. As long as basses are made out of wood, no two can/will ever sound exactly the same. Which is why, out of some 2 dozen basses, I only have 2 pairs - and I never expected them to sound the same. I would have been amazed if they did, and would do my best to make them sound different from each other, anyway. Clones scare me...