As a starting thought on this page, it is my view that we learn in three very different but obviously interconnected ways :
1) SOUND We learn by having a clear intention of the sound that we want to produce. If we don't have this clear intention then we are not going to produce a clear sound. This is not so obvious on piano as it is on most other instruments but it is just as if not even more important.
2) PHYSICAL MEMORY We learn by repetition. Sometimes - to adults especially - this repetition will feel endless and not sufficiently productive. But in fact there are no short cuts. We have to repeat short passages over and over and over again. We have to repeat them endlessly in one hand. Wew have to repeat them endlessly with the other hand. And then we have to repeat them endlessly - and at a slower tempo - with both hands together. The whole process is painstaking and takes a lot of time. But there are no short cuts.
3) STRUCTURAL UNDERSTANDING OF THE MUSIC We learn by understanding the structure of the piece that we are trying to play. This might be at quite a simple level, i.e. 4 phrases of 4 bars each with an A - A - B - A patgtern. Or it might be something much more sophisticated. On the micro level we learn by iunderstanding that a combination of various E flats, Gs and B flats means that we are playing a chord of E flat major. If we are in the KEY of E flat major we learn that other chords such as A flat, B flat 7, C minor and F minor are the most likely chords that we will find. (Obviously here I am talking about tonal music)
Our learning at the piano is a combination of these three learning modes. We may switch between them several times during a single practice session, but if we are not engaged with all three modes then we are ultimately going to be very limited in our progress.