When an electric guitar is connected to an amplifier with distortion, the open strings will make noise unless you are touching them. I used to think that while playing the electric guitar, players had to always make skin contact with all open strings to avoid those noises. However, I just did an experiment and now believe it is not necessary to always make skin contact with all the open strings.

This is the experiment I did:
I noticed that when I tap the back of the neck of my electric guitar with enough strength to move the neck, if I'm not touching any string with my skin, all the open strings will make some noise. However, if I do the same tap while I play a note, my amplifier will not reproduce all those noises, it will only reproduce the note I'm playing.

Questions:
-Does this mean that if a note is playing, you don't have to make skin contact with open strings to mute them?
-If I'm playing a part of a solo that all the notes are in the first string, I do not have to mute all other 5 strings by making skin contact with them?
-Is my amplifier "unique" or do all amplifiers and audio interfaces work like this?

Your gain is too high.

I'm not exactly sure how it works but when you are fretting a note it tends to hold prominence over string noise, the string noise is still there though. You might not notice it while playing, but when recording it's much more obvious. I've recorded things that sounded fine and then realized there was a very noticeable static and noise behind the actual riffs, which has to do with gain.

I doubt your amplifier is unique for this, as I said you should probably turn your gain down. There are methods of using that much gain and dampening the effects of undesired noise, but if you're just practicing I suggest just turning down the gain. When recording there's things like noise gates, compressors, and string dampeners, but again I would suggest looking into just turning the gain down rather than using any of those.

Also, with distortion and any gain there will always be noise when the notes are not muted, though I assume you're talking about it being too much.