Set the Align parameter of the Lathe modifier to Min. Increase the number of Segments for a smoother geometry. Don't overdo it, because this also increases the number of polygons/calculations. Notice the "dirty" geometry lathe creates at the center of the glass.
Check Weld Core to clean the "dirty" geometry. Your wine glass is done! That was so easy, wasn't it?
For the second type of glass start with a Box 20 x 20 x 5 units (length x width x height).
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