A few points:
A tone has three basic moments in it's lifespan
1) attack
2) body
3) decay
Everything you do in preperation to strike a key on the piano affects it's tone.
You cannot change the characterists of the "body" of a tone with the fingers once you have pressed the key.
You can change the characterists of the "body" of a note by introducing pedal. As mentioned by Berrt, it introduces sympathetic vibration of other strings.
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What about the difference between striking a note with pedal and keeping your finger on the key, versus strinking a note with pedal then removing your finger while holding the note with pedal? Yes they do sound different, but why?
I have done a bit of experimentation with this. Many teachers say that leaving your hands on the keys, gives more focus to the tone as opposed to holding the note with just the pedal. They are correct in saying this. Remember you can't change a tone with your fingers after you have struck a note, so why does leaving your finger on the key sound different? It is not the fact that you have left you hand on the key that changes the tone, but rather the mentality of your prepration before you strike a note.
I have noticed that we prepare to strike notes differently weather we indend to pedal them or not. If we intend to pedal, we know that the pedal will support a lot of the note's body and we compensate, by playing a bit less (this is a bit hard to describe). If we intend not to pedal, then we intentionally strike the note with more focus knowing that our fingers are supporting the full weight of the tone. Thus when we strike a note with pedal and intention to hold it we are actually using more focus in the preperation to strike, as opposed just tapping the key and letting the pedal do the rest.
I hope that made some sense
