There are two version of this piece in the Piano Street sheet music library.The original version is by far the most commonly known:https://www.pianostreet.com/piano_sheet_music/Clementi-1426/Sonatina-opus-36-1.htmlThe version you are reffering to is Clementi's 5th revised version:https://www.pianostreet.com/piano_sheet_music/Clementi-1937/Sonatina-5th-revised-edition.htmlThis later version is, as you mention, using a wider register. One could assume that this is reflecting the development of the instruments during Clementi's lifetime.I hope this dispels the confusion!