Weirdly, as an en_GB native, neither of these seems wrong to me. I suspect one is British and one is American, and too much TV has driven me to accept the American one.

"i play piano" - i know how to play piano "i play the piano" - i am playing the piano

that is just my intuition as native english speaker, but the former cojld also mean the latter and i have seen it used like such before.

With context these can mean different things. You might also play a piano, or hire either a player piano, or a piano player.

If you are answering which instrument you play, it's the former, but if we are talking the profession it's the latter, because you don't say then that you play a piano.