The music is inside the musician and it comes out through whatever instrument that they feel most 'comfortable' playing!!
Jazz or Rock is quite different but Rock is often distorted crunchy sound and Jazz is more 'Clean' and articulate, and a PRS can easily do both!!
The difference is much more likely to be down to the 'Rig' the Guitar is plugged into - the Amp, the pedalboard, even where the mic is placed have a LOT to do with the recorded sound, more than the guitar associated with it and at the end of the day, most musicians play the guitars they do because they feel most comfortable with it and it works for them.
Unless you are chasing a very specific tone that 'only' a specific type guitar (12 string, Strat, Les Paul, Tele type) recorded by a famous artist like Vai or Hendrix, then maybe you need a 'specific' type guitar to Chase that tone, but ANY guitar can be used to play Hendrix - they all have the same notes and will be played the same way - even if the tone you have is 'different'
When Famous Artists do 'covers' of Famous Songs, they often use their favourite guitar and 'tone' rather than try and 'copy' the OG artist. Al Di Meola is a famous Jazz Fusion musician who used PRS guitars so ANY guitar can be used to play ANY genre. It's in the 'musician' and the guitar is the way to get the music out - the 'voice' or 'tone' of that is more about the individual preference and their Rig as a 'whole'...
A PRS Hollowbody isn't just for Jazz, it Rocks too. A Solid body PRS doesn't just Rock, it does all the genres too.... It's more about whether you are chasing a specific tone or can find their own tone to suit the rest of the Band when you play Jazz or Rock with them. If you are learning to play both, then ANY guitar you feel most comfortable playing works. They'll all have the same notes - it should be more about do you want/need a tremolo or fixed bridge than will it work for Jazz or Rock...
Jazz and Rock is in the Player and the guitar is just what they use to get that out! Its then down to them to decide whether the 'Rig' gives them the 'tone' they want so it sits in the 'mix' with the rest of the band just the way they want it. It's only if they are chasing a 'specific' tone that only a certain guitar can do, that's different because its 'specific' but in general ANY guitar will do ANY Genre of music.
Acoustic is the same - despite all the different woods, styles etc that affect the sound, they all can do 'Jazz' or 'Rock' too - same with Electric.