Briefly, the Mannlicher Schönauer 'sporting rifles' and the '1903 Greek' or Y1903 have shared roots in the M1900. Original Steyr built (not 'English' or other custom shop jobs) M1900 rifles were prototypes made and marketed in effort to obtain desirable and lucrative military contracts.

Due to their high cost and other factors, the only significant contract awarded to the MS was with Greece in 1903. The Y1903, Y1903-14, and other 'Greek' MS have this contract as their shared origin.

There seems to be disagreement among some, but it is said that all 'M1900' Mannlicher Schönauer rifles and carbines are actually modified military prototypes or barreled actions. It was only after the Greek contract had been awarded that the Mannlicher Schönauer sporting rifles went into production at Steyr for the civilian market.

It could be said that the Mannlicher Schönauer M1903, M1905, M1908, M1910, M1924 are refined, cultured, siblings of the Y1903 and other 'Greek' variants. The internal parts of the M1903 and the 'Greek' rifles are completely interchangeable.

Some photos:
Greek MS

Here is a lengthy (over 1 hour) and (very) detailed video regarding the 'Greek' MS with lots of history and background. He actually gets to the Mannlicher Schönauer itself (M1900) at ten minutes in and brings out the 1903 at 22:30, the 1903/14 at 33:45, Carbine (1903, 1930) at 39:20, the 'Breda' at 47:07, more about the 1930 Carbine at 48:21, and at 54:55 Mae "can't believe it's not butter". -
Greek MS Video