Oh, yes, definitely, on all counts. Sheet music might be a transcription of one particular recording or performance, or an edited and selected mix of a number - or, more frequently, a simplified outline of the melody and highlights aimed at the middling pianist.

Having said that, there is no doubt the odd Blues pianist who settles on a specific arrangement and sticks with it note for note, but that would be the exception. Blues is essentially improvisation within a simple but (usually) rigid chord structure.