Confusion about different versions of the main theme song

You notice throughout the movie that there are different variations of Morricone's main theme used in many scenes. However, there seem to exist two completely different versions, not simple alterations, of the track itself. On my Morricone platinum album is a track with a duration of 4:18, which sounds like the one used in the most recent english dvd and bluray releaes as well. However if you google long enough or search on youtube for "A Fistful of Dynamite HQ Audio" you will notice there also exists a composition of 4:36, which opens in a darker mood with the addtion of a drum and many other differences. It sounds like it was made as a cover version or...and this is really my question here, could it be that this is from a supposedly "original" (italian?) score compared to modern releases of the movie?