I saw that you uploaded clean recordings so I did a little experimenting. I ran both recordings through Guitar Rig with a high gain sim (Guitar Hero, I think, but I turned off the noise gate in GR and disabled the noise suppressor in the rack). Both recordings, the UR and the Focusrite created the same amount of hiss and noise, during playing and when you stopped.
Then, I opened a Cubase project, imported both files and added the same VST amp Rack sim to both (rectomate) and disabled the gate, of course, and both recordings are noiseless as far as I can tell.
Is it possible you have a noise gate on one of them and not the other? Some amp sims are very noisy (even with the guitar volume turned all the way down) but I found both of your recordings equally noisy in those sims.
I tried again in Cubase and loading Guitar Rig with the Gratifier (GR Gate turned off) and cranked the gain all the way and got some noise but they were equal in each recording. I also opened both files in the sample editor and zoomed all the way in vertically and looked at the ends of the audio (after you stop playing). Both are basically flatlined except the UR has a little “bump” at the end where you probably bumped the guitar or something (but it’s not noise).
So I think there is something different in the two different setups because it looks like they are both recording very quiet audio with no playing.