Aubeline Brandamir 

The mapping statuses between the XLF and the SDLXLIFF are set in Project Settings > File Types > XLIFF > Segment Status Mapping. You can also set how Trados Studio writes its own statuses to the XLF file when you are done. Below is just an mapping example, just can tweak it as it suits you:

Aubeline Brandamir said:

but when I open the files I note the segment statuses in Studio are not the same as the ones in XTM

You can see that statuses differ, at least tey have different name, but you can mapp them as shown above in the animated image.

Aubeline Brandamir 

The mapping statuses between the XLF and the SDLXLIFF are set in Project Settings > File Types > XLIFF > Segment Status Mapping. You can also set how Trados Studio writes its own statuses to the XLF file when you are done. Below is just an mapping example, just can tweak it as it suits you:

Aubeline Brandamir said:

but when I open the files I note the segment statuses in Studio are not the same as the ones in XTM

You can see that statuses differ, at least tey have different name, but you can mapp them as shown above in the animated image.