We are having a discussion over in the Oz members' thread re oxford cloths.
I was looking on your site, and I believe that those currently labelled "Royal" oxfords are actually "Pinpoint" oxfords.
They have the fine square weave rather than the diamond weave, and don't have the sheen of a Royal oxford.
I might be mistaken, though. I'm not 100% sure of the difference between each.
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In my understanding, Oxofrd is a standard consistent weave.
The difference in pinpoint and royal pertain to:
1. The count of the yarn used
2. The construction of the weave. The Royal oxford is tightly woven which gives it a sheen.
At times, if there is a difference in the count of the warp and weft yarns, the structure can appear different, like the diamond and square you mention. As far as I am aware, that is not a factor in calling it pinpoint or royal.
Will be glad to be corrected though.