You may wonder about my title. If one is a pianist, isn't one automatically a musician? Not necessarily.
I've encountered many people who are pianists, that is, they play the piano with some degree of proficiency. Some even play with emotional involvement and expressiveness. But to be a musician, I believe, requires something more.
To be a musician, to me, means a broad and deep understanding of music. For instance, many people coming to me for lessons who have played and/or had lessons previously do not know the basics of how our music (Western music) is constructed. If I ask them what key a particular piece they have played is in, they don't know. They may not even know what it means to be "in a key." They may have practiced scales as an "exercise" but don't know that scales are our basic tonal material, our "alphabet," if you will. Some have told me they never knew why, for example, a given piece had to be played with all F-sharps instead of Fs; they never knew that means it is in the key of G Major (or E minor). They may have read and learned to play "the notes" of the piece, but they don't understand what is behind the notes. If I ask them to identify the basic harmonies (chords) of a section of the piece, they can't; in fact, many do not even realize that chords are the basic building blocks of most of our music. To me it is just unfathomable how one could play a composition and somehow think it is just an assortment of notes, and not realize the underlying structures which make it a unified whole.
To be a musician also means a broad range of musical skills. Again, many people have learned to read music and can play the notes as represented on the page. But if I ask them to play Happy Birthday by ear and harmonize it with three simple chords, they can't do it. How can this be? The Chopin Nocturne they just played for me is much more complex than Happy Birthday, but they could play it because the page told them exactly which notes to hit, and when, and they simply "obeyed." But if they have to play music where the knowledge must come from within them, they are unable. I cannot call this person a musician yet. For this reason, I have all my students play simple music by ear, learn about chords (simple first, then more complex, such as 7th chords) and their relationships to each other, how they "progress" from one to another. A real musician can't be comfortable playing in just the key of C and maybe one or two others; a musician must play in all keys with ease. For this reason I have my students do a lot of transposing.
Not everyone wants to be a composer. And not everyone wants to improvise. But any musician should certainly be able to sit down at his instrument and play something without the need for written music. (There is a joke among jazz musicians that goes like this: How to do you get a musician to stop playing? Put sheet music in front of him.) I make sure all my students can improvise at least some simple melodies on a simple chord progression, and have it make sense. (I show them how to choose a short motif and build upon this, rather than just randomly search for notes.) If you can only read music and can't do this, it is like being able to quote from a book but not able to construct a sentence of your own.
I consider it my mission to help create musicians, not just people who can play the piano. Music itself is an incredible mystery: how it makes sense to us, why it moves us the way it does, why it has become such an important part of life in every culture on earth. Yet, a great many aspects of music can be understood and grasped by our minds, and this knowledge does not lessen the mystery; I believe it increases the sense of wonder we have for music. The more you know, the more marvelous it is. If you play an instrument, I encourage you to strive to be a musician.