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Yup they are the II series tired. I verified today. I have no idea what the difference is but I'm very happy with the winter performance in these snow covered roads.
Here's the response I got from my DS regarding Tesla Winter Tires:
Winter Wheels/Tires
The 19” Winter Tire Set comes with Pirelli Sottozero II. This is the tire that Tesla has tested with the 19” wheel and it has passed our requirements. If you would like the Sottozero III you can absolutely purchase them elsewhere, but we cannot install them on your wheels.