Yes, there are some differences. Do they make it sound different? Yes, slightly but its nothing to get your panties in a twist over IMO.
I have a 1966 Daphne blue (well, its half green after 44 years...its older than me:) ) Mustang and when it had the stock pickups (which suck bad like all fender pickups under 8k) in it it sounded pretty close to a stock Japanese Mustang.
Vintage finishes are nitro, except 70's(+possibly very late 60's)ones and so forth.
Vintage pickups tend to sound a tad better although they all sound like #### to me personally.
Vintage bridges are better constructed and look slightly different.
Vintage vibratos have pat pending on them.
Some vintage ones like mine have celluloid pickguards not plastic.
Vintage ones have CTS pots not the mini Japanese ones (nothing wrong with them at all IMO).
Vintage are not metric like the import ones.
Most RI's don't have shielding plates.
etc etc
However, if you want to buy an import reissue the fender mustang is the closest to original spec'D guitar Fender Japan ever made, especially the 65 RI which is even closer than most other RI's.
Fender japan's jaguar is second and the jazzmaster is last as it differs so much from an american jazzmaster about the only thing in common with the American model is its name and shape.
Even the production jagstang is different than Kurt's, which were not Japanese made but American custom shop made.
And all this historical crap aside, the Fender Japan Mustangs are sick guitars!!! Vintage does not always mean better, sometimes it does but not always. My 66 sounds better acoustically than any MIJ/CIJ I've played and it sounds better plugged in too but that's just my opinion.
I've come to absolutely #### hate poly guitars (they do sound different than nitro believe it or not, I never believed it for years but they do indeed) so I have an aversion to them but if a CIJ Comp Blue mustang came up I'd still buy it in an instance. I like the feel of poly necks, I just hate the sound of poly guitars in general (massive generalization present!). The poly vs nitro thing is another topic (should I say argument) altogether! 😁
Bottom line: They are great guitars, sound good with some single coil sized humbuckers in them (which are drop in replacements) and they are cheaper than you can ever dream of getting a vintage one for!