What's the difference between Pinot Grigio and Pinot Gris?

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Dear Dr. Vinny,
What’s the difference between Pinot Grigio and Pinot Gris?
—Louis B., Port Louis, Mauritius
Dear Louis,
This is a little different from some of my recent questions on the differences between Cabernet Sauvignon and Merlot or Sémillon and Sauvignon Blanc. To answer those questions, I explained how they were two different grapes (and wines made from these grapes). But in the case of Pinot Gris and Pinot Grigio, we have a single grape variety going by two different names.
This happens sometimes in the world of wine—the best-known example may be Syrah and Shiraz, which are both different names for the same grape and wine. And just as with Syrah/Shiraz, Pinot Gris/Grigio can also refer to different styles of wine.
Pinot Gris, which has its spiritual home in France’s Alsace region, is typically rich and on the sweet side, with notes of spice and tropical fruit. Pinot Grigios—like the ones from northeastern Italy—are made in a lighter, crisper style, with citrus flavors. Winemakers from outside these two regions often evoke the style they’re going for by choosing one or the other version of the name.
—Dr. Vinny