I have studied classical music for a few years. I have a good understanding of basic harmony and I can play some pieces of acceptable difficulty on the piano (sonatas by Mozart or Beethoven, nocturnes by Chopin, etc...).
But here's the thing: I can't do things like sitting at the piano and start accompanying myself while singing some song that I know (not necessarily song written for piano)... more precisely: I can do it but the result is far from natural and musical... I'm like a robot playing the chords in block form or arpeggios but in a rhythmically trivial way. The result is awful.
This is something I can perfectly do with my guitar (even when it is not my main instrument and I only play it like a hobby). I know it is easier, but I can take my guitar at any moment and if I know the chords, start playing and singing a song that I've never played before and the result is completely nice and musical. I don't start playing chords in blocks at every quarter note like a zombie...
I've just seen this video that can make the point explicitly (if you allow me the comparison... obviously I'm not in the same league as them...). I know this song but I've never played it. I know that I can bring my guitar here and do "exactly" what Ed Sheeran is doing (again, sorry... you know what I mean), but I feel that in order to do what Tim Minchin is doing, I should practice a lot before I achieve it. I know Minchin's part is harder, but I'm a pianist more than a guitarist!
I don't know if it's related (I suppose it is) but I also have problems improvising at the piano (simple things, I'm not talking about improvising jazz). I have the theoretical background to do it, but when sitting in the piano trying to play something is like I'm blocked and need a lot of time to switch between chords. That is, I don't have them in my "muscle memory" as I do on the guitar (again, I know that in the guitar case this is easier... but piano is my main instrument and guitar is not).
Another detail that might be relevant is that I have very poor first sight reading at the piano. The reason for this, I think, is lack of practice. For that I have a pretty strong memory and then, when I start studying a piece, I usually memorize passages of it way before I play them fluidly... hence, I've never felt the real need to play while reading (I know it is not a good habit and I should work on this
Someone could bring me some light on this issue?