The simple fact is that the R designation exists in European nomenclature because there are a lot of rounds that have both rimmed and rimless counterparts.
These are, of course, primarily sporting rounds, but some, such as the 7.92x57 and 7.92x57R or the 7x57 and 7x57R, have done double duty as both military and sporting rounds.
For rounds for which there is no rimless counterpart, the R is often still included just as an additional identifier even though it's not absolutely necessary.
"Dare I ask what your opinion is on the Kynoch "Flanged" rounds I have?"
Well, if you truly want my opinion, they're flanged.
As for the 6.5x53R, well, in Europe there WAS a rimless 6.5x53, a short-lived military cartridge called the Daudeteau, which was used for a short time by the Lee Navy.
It gets more confusing when there are multiple cartridges of the same nominal caliber, case length, and both are rimmed.
8x50mmR and 8x50mmR.
Which one is the Siamese round and which one is the Lebel?
That's when the final part of the identification comes in -- the generally accepted name, either Siamese or Lebel.
Semi-rimless... That term came about for a peculiar reason... Rimless cases are always assumed to headspace on the case shoulder. Rimmed cartridges are assumed to headspace on the rim.
But there are a few cartridges that have discernible rims, such as the .225 Winchester, that were designed so as to headspace on the case shoulder. That's why they're called semi-rimmed...
