One way to look at it is that the professional's repertoire is 30,000% or 40,000% larger than the amateur so they have tens of thousands of hours more development. A very advanced amateur's entire lifetime repertoire can be learned in under a single year or maybe two (and this may be overly conservative, probably just one year is enough) for a top professional like a Daniil Trifonov or Grigory Solokov. So the phrasing and finer muscle control, sensitivity to the escapement, ability to fire the wrist, familiarity with wider ranges of motion with the elbow and more extreme wrist rotation, moving the torso, pedalling, ability to voice with the 4rth and 5th fingers trained in all sorts of double note textures and variations -> all those things will be learned and refined much more thoroughly as you go through the repertoire. Even if a piece like the Chopin B flat minor nocturne is within a lot of amateurs' level, the professionai wll still sound better because he or she has performed most of the ballades, scherzi, polonaises, both concerti and both sonatas, a lot of the other nocturnes, waltzes, mazurkas, etc.Tons of amateurs play the Moonlight sonata or Pathetique but the professional who's played 4 of the Beethoven concerti, and 20 of the other sonatas or even all 32 sonatas will still sound better. A really advanced amateur might play something like the Liszt HR2 friska or La Campanella well but professional who has played the Liszt grande fantasie on la clochette de Paganini, El contrabandista, all the opera transcriptions, will perform it with a lot more freedom and bravura because they cut their technique on much harder jumps than in the easier Liszt, and because of the higher margin of safety they can divert their conversation more to color and clarity, and no longer have tendency to cover up flaws with heavy pedaling etc. I suspect that psychological freedom to use the pedalling cleanly is a huge factor in this. If you can play a piece at a high level and clean up the pedalling - this alone and nothing else - will set you apart and allow listeners to wonder if you're professional.
Very well put. It's hard to get around that you need a large quantity of experience. Quantity can be achieved by 1) playing many pieces that are around your level (i.e. you can learn them in 1-7 days) and 2) developing your technique so that the pieces you can learn in 1-7 days become significantly more advanced. The very best pianists could learn concertos and the like in a few days and then perform them successfully. That's not feasible for everyone but it's good to be aware of what's possible.
I have been watching a lot of videos of performances recently, and there seems to be a clear difference between the seasoned pianists (e.g. competition winners) and the amateur ones. Even though the dynamics and articulations are observed in both cases, the seasoned pianists' performances just seem more "musical". I think I belong in the amateur category. Whenever I listen to my performances it just sounds "sloppy" even though I played all of the musicalities I've planned. I don't know if this makes any sense, but if it does, do people have any tips on achieving this musical maturity and what the "difference" actually is? Thanks so much.