Does the remastering make the notes more clear, clean up the background noise, or both?
Remastering is an art, not a simple push-button process. There is a lot of technology available today which can get rid of noise in the background, which will clear up how notes sound.
It's also possible, that there may be segments of audio which just didn't sound good on the original, and they can be re-recorded and inserted into the mix as part of the remastering process. If they are working with original masters and multi-track recordings, then there will be a lot to work with and the ability to insert a new recording of drums or a guitar is fully possible.
For some remastered content, the goal would be to leave things as untouched as possible, but get rid of noise, and clean up the sound of vocals and instruments as much as possible without impacting anything else.
For OTHER remastered content, it may be close to a complete revamp of the sound. With new instruments, and potentially some new vocals put in. Levels may be adjusted significantly to make something stand out. This should generally be done due to listener feedback over the years, or artist feedback, or both.
Drawing a single line down the middle and saying "This is remastering, but that is not!" is incorrect. There are many ways to approach a remaster, and at times, any of them may be the best way of doing things.