I think the Carcano models are some of the most confusing out there. There are M38 rifles that are chambered in the original 6.5 caliber, but then it would have the designation M91/38.
The M38 in 7.35 has a small latch on the buttplate that stores a cleaning kit that I don't think the TS has. And also the finger grooves on the stock are a feature of the M38 and not the TS rifle.
Check out this link: http://personal.stevens.edu/~gliberat/carcano/