There are four time zones from one endpoint to the other including the end points, three time zone transitions between the end points, and two time zones that are between the time zones containing the endpoint.

I'd be hesitant to call any of those numbers wrong when offered as the number of timezones between SF and NY, either three or four probably match the most common uses specifically related to timezones, though two would probably best match the usual use of "number of Xs between Y and Z".