CLASSICAL or JAZZ
You might be thinking, "Wait a minute, David! Classical and jazz are not the only kinds of music there are. What about gospel, rock, pop, country, hip hop, R&B, film music, Broadway, video games, bluegrass, folk, etc??"
And you're right, there are many many types of music you can play on the piano. However, in this case, you would be describing genre. When I talk about classical and jazz, I am talking about the style of learning NOT the style of the music. As you'll soon see, you can actually take a classical approach to learn jazz music, and a jazz approach to learn classical music. For any of the styles/genres listed in the previous paragraph (in addition to classical and jazz), you can learn the music with the CLASSICAL APPROACH or the JAZZ APPROACH.
Confused?
No problem. Let's define what each approach means, and it will be clear.
THE CLASSICAL APPROACH
The classical approach to learning music is that what you are going to play has already been fully transcribed as sheet music. What the right hand plays, what the left hand plays, the exact rhythms, the exact chord voicings, usually the dynamics, and sometimes the fingerings and pedalings have been fully notated. A musician comfortable in the classical approach is asked to learn Blackbird by the Beatles. He or she will go order a book of piano transcriptions of the Beatles tunes (or that specific song) and start reading the music and learning how to play it.
THE JAZZ APPROACH
The jazz approach is to use as little sheet music as possible when learning music. This falls in a variety of levels. (1) On the extreme end, learn by ear. That is to say, listen to what you want to learn, and try to play it based on how it sounds. (2) Lyrics and chords. Almost any pop song can be googled followed by the phrase "chords and lyrics" or "lyrics and chords". You'll get the words for each song with the chord symbols listed above. If you know how the music sounds, you use this to instruct what you should be playing. (3) Lead sheet A lead sheet is a single line of sheet music, usually for the right hand melody, but with chord symbols over the notes.
The person wanting to learn Blackbird by the Beatles in the Jazz approach will use one of the three approaches above.
The person wanting to learn Blackbird by the Beatles in the Jazz approach will use one of the three approaches above.
To give a full example: Here are samples of lead sheet versions of a jazz tune (Begin the Beguine) and a classical piece (Beethoven's Moonlight Sonata).
As you can see, it's a minimal amount of notation with chord symbols above. The performer will have to interpret the chord symbols to play something that sounds like what is expected.
Now here are fully composed sheet music excerpts of the same two pieces.
With the fully-scored sheet music, the guesswork is eliminated, but the amount of reading required is increased, so that brings me to the next point.
As you can see, it's a minimal amount of notation with chord symbols above. The performer will have to interpret the chord symbols to play something that sounds like what is expected.
Now here are fully composed sheet music excerpts of the same two pieces.
With the fully-scored sheet music, the guesswork is eliminated, but the amount of reading required is increased, so that brings me to the next point.
PROS OF EACH APPROACH
Classical approach: (1) If you want to spend as little energy as possible in figuring out WHAT to play, there is no substitute to the classical approach. Well-written detailed sheet music tells you all you need to know about playing the music the same way someone on another continent in a different time period would play the same thing. HOW to play it is a different challenge, but if you are good at reading sheet music, you can just play it. (2) If you are to work as an accompanist for hire at theatres, churches with traditional worship services, music or dance schools, or with classical chamber ensembles, you MUST be good in the classical approach to learning music. So much of that work is sight-reading.
Jazz approach: (1) A lead sheet often takes up less than half the amount of pages than regular sheet music, and this means that you can carry more songs with you. This is especially important if you're playing for parties, dinners, or other casual settings. (2) If you want some freedom and input in the creative process (for example: maybe you want to play the left hand with a different pattern than the original version), then the jazz approach makes that possible. You may not be the composer of the song you're playing, but you can instantly become the arranger. You also are not prevented from learning a piece simply because you can't find a good version already composed on sheet music.
TOOLS NEEDED TO LEARN EACH APPROACH
Classical: Note reading skills for treble and bass clef. The faster and more accurate, the better. Sight-reading skills are imperative if you want to play more music with less practice. Memorization, if required or desired, is more challenging on this approach because you are trying so hard to get what's on the page. Technical skills and theory skills improve odds of success. The player needs to save money because well-written sheet music can be expensive.
Jazz: Compared to the Classical approach, the player on the Jazz approach needs a much higher understanding of chords - what each chord is, how to build them with various voicings, how to invert any chord, how to change smoothly from one chord to another. Technical ability with scales and arpeggios are equal to what is required from a classical player. The player needs to learn styles and patterns as something that can be plugged in when learning a piece. The player needs to learn to be creative to have the most success in this area (in other words, don't try to play the piano EXACTLY like the artist in the recording, but be willing to add your own variation). If you're not going to use lead sheets, the jazz player needs to develop a very good ear for hearing music and figuring out how to play it on the keys.
Special note on techniques: Classical and Jazz approaches encourage the most progress you can make with scales, chords, and arpeggios. Jazz musicians (and for once I'm talking about the true genre of jazz) prioritize the concept of All-keys practice. In other words, any technical exercise you learn gets transposed to all keys. The same is true of songs known as standards. The good jazz player can take Begin the Beguine with the lead sheet above and play it in that key (of C major). The elite jazz player can change it to any of the other 11 major keys.
WHICH APPROACH IS BETTER?
Hopefully you can guess the answer to this, but... there is no right approach or wrong approach that covers everyone. The right approach is the one that you either have a strong inclination for or are willing to invest in the skills needed to do well. Also, think of your situation. Are you playing for traditional churches, school ensembles, theatres, or other places based on classical sheet music? Or are you playing just for fun, or with a band of some kind, or for dinners, parties and other such events?
And here's another answer.
How about...both! If you have any kind of career aspirations in music, I strongly recommend getting some degree of comfort in both approaches. Two things are true: not every professional musician bothers to learn both approaches, and most who do still prefer one way or the other. But a pianist who can alternate between playing wedding music off sheet music with a flute soloist and then go learn a Journey song off a recording with a lyrics and chords sheet to play with a band will have all kinds of work. The theatre is where I've had my most performance work in the past 10 years, and I've been asked to read music off at least 10,000 pages by now. But I also have been asked if I can listen to a recording that's different than the sheet music and learn to play it like so.
Also, you don't necessarily have to learn both approaches at the same time. I will add, however, that there is an ample amount of anecdotal evidence to suggest that getting a foundation of the classical approach and then switching to the jazz approach is more widely successful than trying to do it the other way around. This is why I and so many other teachers start every beginning student the same way. At some point, I want you to choose a course, but I want that course to happen after at least getting started in a classical approach. Having even a small grasp will help you learn other music regardless of the approach you take.