It depends on the model and how closely you look at the bass.
I own a Squier Matt Freeman, an AVRI 57P and an AS Jazz.
The bridges are all different. The Squier has the high mass they've been using on the CV series. The Jazz has the US string through high mass bridge and the AVRI P has the bent plate with the threaded saddles.
As already stated the control knobs on the Squier are pressure fit and the Fender models have set screws. The knobs themselves feel like they are higher quality on the Fenders. The Squiers seem like the metal used was poured into a mould. The Fenders look to be machined metal. (fwiw)
The scratch plate on Squiers can be cheaper material too, with some warping. My Freeman pickguard is a bit wobbly. I had a VM Telebass in the past and it also had a PG like that. 3ply black and not totally flat. Fenders have always been flat. My Jazz PG is flat and in the past I've had an AS P and a Hwy1 P and both had flat PG. Nit picky I know.
The neck plates are different too. If I remember correctly, my Squier has "Squier" scribed into it. I think the AS Jazz has "Corona, Calif" on it and the AVRI has the serial# punched into it.
Some people think the frets are rough on Squiers compared to Fenders but i can't really tell. Maybe very slightly. The neck on my AVRI feels amazing and the AS Fender is really nice too. Squier is nice but maybe a bit less nice compared to the Fenders (if that's possible). AVRI neck is gloss nitro, the AS Jass is satin poly and the MF Squier is glossy poly.
Tuners can be different also depending on the model.
AVRI '57 Precision | '11 MIA Jazz Bass | Genz-Benz Shuttle 6.0-12T
Official Fender Precision Bass Club #615 | P-Bass Club #642 | Fender Jazz Bass Club #853