Given the prominence of Brilliant as almost a brand label on the posted image of the box, there might be some kind of marketing psychology involved, and not merely a sheen identification. Hard to say. Let me explain :
The "Brilliant" name began with Brilliant Bromide graded paper made in France and marketed by Zone VI Studios in the US. It was an extraordinary paper.
But when Zone VI was bought out by Calumet, the Brilliant label passed on to them, but with respect to a quite inferior product made for them in England by Ilford. Subsequently Calumet itself went out of business.
In that manner the "Brilliant" name might have been inherited by Ilford. MGWT is itself a superb product, but variable contrast and no relation to the original French Brilliant paper. If MGWT had existed contemporaneously to the original, and they had applied that term, they probably would have been sued, at least if it was capitalized and printed bold. But now there's no kind of overlap capable of causing confusion. Here in the US it's simply been labeled, "glossy" (in small print). But I've thrown out all my old empty boxes, so can't check those.