The Turk M1903 and the M1938 are two completely different rifles. The "M1938" is a 'standard', that many older rifles were upgraded to, as well as later production rifles. It includes the earlier small ring Mauser types upgraded.
The M1903 was the Turk's first large ring Mauser rifle, a variant of the German G98 long rifle.
A look in Robert Ball's "Military Mauser Rifles of the World" gives the history of the Turkish Mausers.
In the late 1930, the Turks began standardizing all their prior Mauser rifles to one basic standard, the M1938 Short Rifle. All original markings were ground off at this time, and the new Model 1938 markings applied.
This makes rebarreling and altering the caliber of Turkish rifles tricky - the older small ring actions won'tbe strong enough for the more powerful calibers.
Also check this website: Turk Mauser
I had thought my own Turkish Mauser was an M1903 - it had the basic features of that rifle - but it proved to be the M1893 action rearsenalled to the M1903 long rifle standard, some years before the M1938 standard was decided upon (making their rifles generally similar to the German Kar98k).
Turkey was one of Gebruder Mauser's best customers for decades, and always tried to keep up with latest European developments while upgrading their older rifles.