I have had experience with this in a slightly different manner, when a profile was made for a particular paper, and there were differences in the printing after I changed rolls after one roll had run out. . I thought I must have forgotten something so I reprinted, then found a scrap from the previous roll and reprinted again. Sure enough there were marked differences.
Knowing that some paper companies have various manufacturing mills around the world, even though all using the same 'recipe', there are bound to be differences between rolls produced from different mills branded under the one label.
I wouldn't be surprised if the different sized media and differnt results in your profile are a result of the same branded 'flavour' paper has been produced in a different location.