I'd like to point out that several sources put the 1893/1938 mausers as 8x57JS (8mm mauser). They are availible from
www.sportsmandguide.com as "8mm Mauser"
www.surplusrifle.com calls it 8x57mm Mauser and has picture of regular 8x57 being loaded and unloaded into one. Note that the original 1893 Turkish mauser was chambered in 7.65x53mm caliber but were later rechambered to 7.92x57mm (8mm Mauser). The 1938 standard caliber was 8mm Mauser.
The fact that no one has seen surplus 8x57R ammo coming out of turkey, and only 8x57 Mauser suggest this as well. And note that Turkey used their mausers until the 1950's when they were replaced with weapons of US origin.(Hogg, 217)
And the model 1938 was just all the mauser rifles that Turkey had reworked into 8mm mauser.
EDIT: I also dug up some more info on 8x57R
http://www.recguns.com/Sources/IIID1c1.html
"There is also 8x57R (or 8x57JR, or 8x57JSR), which is a *rimmed* cartridge for use in German single-shots and drillings. These should *not* be used in rifles designed for rimless cases (like the Mausers)."