Do intermediate musical notes exist?Watch
I noticed that they have notes that don't sound like a Re but don't sound like its sharp version, either, more like in between them.
Any number of intermediate musical notes exist. Between any of those notes, an additional, infinite number of musical notes also exist. You can just average two frequencies to get the frequency halfway between them, then find the frequency halfway between that one and one of the original ones, then keep doing that indefinitely, at any pitch. All of those are valid musical notes, although most are not normally used in our musical culture. A slide whistle, trombone, or violin are capable of playing any of them, although a xylophone or piano are not (unless you do shenanigans like reaching inside and manually damping it in different places).