Playing both piano and organ for years, I must say that there are two distinctly different playing styles needed to be mastered in order to do justice to either.
*Piano-Forte* -- Literally, the "Loud-Soft" connotes the difference in the instrument's name. It is a Velocity Sensitive kaybed and the way you finger that is *all important*. Playihg an organ style keyboard and using organ fingering technique may get the notes out there, but it is indeed going to sound different than playing the same part on a velocity sensitive keyboard, with correct settings and correct fingering techniques.
That said, I think it also depends a lot on the genre of music being played at the time. I have, for example, played some rock or R&B tunes on a MIDI keyboard with no sustain pedal on a few occasions where the stage show or whatever dictated that. Most of those were NOT examples of the piano-forte, though, they were more like examples of cover tunes that weren't recorded by very good pianists in the first place. But for their intended purpose, they work.
**When I first started on organ, after about a decade on piano, the drill was to place coins on the backs of the hands and practice scaling and later on chording, etc. without moving those coins or dropping them. Exact opposite technique from what we do on the piano, which is to move the fingers or whole hand a lot more in the vertical.
**I can't stand those darn MIDI keyboards that leave the Velocity Sensitivity turned on for an organ patch, either. Again, might come in handy for a rock cover where there is no Expression Pedal available, but certainly not very realistic, even when you know what to do and how to mimic the real McCoy.
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"Keep listening. Never become so self-important that you can't listen to other players. Live cleanly....Do right....You can improve as a player by improving as a person. It's a duty we owe to ourselves." --John Coltrane
"You don't know what you like, you like what you know. In order to know what you like, you have to know everything." --Branford Marsalis