But in the real world of music, there are several pieces whereby their original versions weren't written for piano solo -they can be for the full orchestra, or for the pop band. So we need either professional arrangers to arrange them for piano solo playing purposes, or we arrange them ourselves. One example is Tchaikovsky's Marche Slave for the full orchestra. But for play-by-ear musicians like myself, I would rather arrange my own piano version for Marche Slave instead of playing by score on someone else's arrangement. For many pop music, sometimes we don't even have their original scores because the composers/arrangers don't prepare them. Instead, they are produced into their final audio forms (using arrangement software) straightaway.

Your last question is a tricky one. There is a thin line among compositions, arrangements and improvisations. The acid test is really whether the main motiff (melody line or tune) is still recognisable. The arranger can add lots of ornaments to it to make it sound in a different style, but if the tune is still recognisable, we will still say it is an arrangement for that particular composition.

But if it sounds totally different (we don't hear any glimpse of the original song's melody at all), that we can't even say this is an arrangement of that particular composition - so it is on its own (own original composition/arrangement).

However, sometimes the case may not be so straightforward. For example, the arranger can retain the main melody notes, but arranges something completely original say for its long prolonged interlude. Nevertheless we will still recognise that this is an arrangement of the original composition.

Woah....I didn't expect a whole essay, haha. But I do believe that my understanding on the concept is way better now. Though it might take me a while to understand everything, I do think it has been a great help that I appreciate a lot. Thank you!

Haha, this is because you were asking one of the BIG questions in music, just like if anyone asks any of the 7 big questions in economics such as what causes inflation and what causes unemployment, I'm sure the economics lecturer will answer longer than an essay!

A side track to this is: It is easier to get the computer (organ/keyboard) to harmonise for your melody than to teach someone to do so. Likewise, it is easier for the computer to identify your chord (based on your notes played) than to teach someone to do it. Thank goodness the computer is unable to identify the key of a piece of music yet. If it is able to (in time to come), it will indeed be a scary era.