Sheet music contains instructions for making human musicians behave a certain way. There is no sense in which it's a complete description of a musical performance. Timing variations and dynamics are all controlled by the player.

If the score is figured bass, the player will improvise/create a complete accompaniment from a sketch of the bass line and some hints about the harmony.

And it's not necessarily unchanged. The layout of a piano score and a transposed brass line are only distantly related. The notation will be common, more or less, with the limitation that a horn line is monophonic while a piano can play chords.

But the key won't be the same, which means the pitches won't be the same. And many of the expressive markings will be different too.