Actually, its the other way around.

The notes are the same when played, but different when read. A middle C is always a middle C, but the transposition required to play a Middle C on an instrument of higher pitch than another instrument in the same family, gave rise to the system we have now, which allows a musician to play the music as it is written and still sound the correct pitch, due to the composers transposition of the part before the instrumentalist even saw it.

Thats how it is from a composers point of view, and a technical point of view. From an instrumentalists point of view your description is correct, but the instrumentalist would have to apply that differently for every instrument, whereas the composers definition of transposition applies across the orchestra.

^_^ I am an instrumentalist.

Realistically, wouldn't it be that they sound the same if played different notes?

Goodness, how difficult it is to describe.

Haha. Its much easier to describe to people who can read sheet music, but I wanted to give a definition anyone can use.

True. Well I can read sheet music, I'm just unsure how to describe it, you know?

>.>

I've been reading for a while now. =P