Indeed, on a piano, the notes are fixed (you cannot play any note between two notes), so the only "interpretation" a performer can add to an existing piece of music is a change in the timing of the notes, and the loudness (attack) of the notes.
Of course, on other types of instrument, this may not hold.
There's also duration (legato vs staccato) and "smearing" notes to achieve that 'in between' sound. Very common in jazz, rock and blues, but not unheard of in classical.
This is not really so much true today, but adding trills and other ornamentation used to be a central part of performance. Also, on a real piano, the touch each note is played with is far more nuanced than simply "loudness".
Of course, on other types of instrument, this may not hold.