Splitting vertices is unwelding. Combining vertices that are in the same position is welding.

Smoothing of normals across polygon boundaries happens when they share vertices, i.e. when they are welded. Smoothing cannot happen if two adjacent polygons do not share welded vertices, but instead have each their own copy of the vertex points.

Welding and unwelding indeed does change the vertex count unless the tool is capable of leaving unconnected vertices after a weld. Most do not.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)