However, modern collectors and enthusiasts would like to tell the variants apart, and so they started assigning labels to what they’ve found, see Wikipedia.

White did not actually assign their machines a particular model, they were all VS machines in different variants. They were all made some time between 18, they all have a long arm vibrating shuttle design, but other details vary. One is made by White (model VS2-b), one is by Jones (Medium CS) and one by A.G.

I have three machines of the White vibrating shuttle design.