Think of the piano you are playing as a dance partner with a unique scope of capabilities. And, because each piano is different, you must appreciate these differences and be flexible in your approach to the music.
The three most important differences are the action, volume, and dynamic range.
The Action. Piano actions range from extremely heavy to extremely light and have an enormous effect on how your body feels as you play. Heavier actions provide more inertial feedback than lighter actions, but tend to be slower. Adapting to a given action can be a challenge. What is the “sweet spot” of interfacing with this particular instrument? The goal is to neither “overplay” nor “underplay”. Heavier actions tempt us to “overplay”, working harder than is necessary by pushing and throwing our arms at the keys. Lighter actions tempt us to “underplay”, being timid and holding back.
Volume. Some concert grands have enormous sounds that can overwhelm a room, while some spinets have tiny sounds that can be swallowed up by a room. It is tempting to “overplay” a soft instrument in order to get more sound out of it and “underplay” a loud instrument in order to keep it down. Of course, setting the volume is a non-issue for electronic instruments.
Dynamic Range. Every instrument is capable of producing sounds only between a certain softness and certain loudness. Don’t try to get “more sound” or “less sound” out of an instrument than it is capable or you will wear yourself out and become extremely frustrated. No matter how developed your technique and sensitive your musicianship, you will not get the same range out of a spinet that you will from a concert grand. The goal is to work with the instrument, not against it.
Finally, be careful that you don’t just learn to play a piece based on the peculiar sound or action of a particular instrument. Your mastery of a piece should be such that you can play it on any instrument.