Is the start winding on the second drawing supposed to be in series with a run winding?
Yes, it is. It is a 115 volt winding so has to be in parallel with one half of the run windings (for the high voltage connection).
The two run winding sections in series act as a voltage divider to split the 230 volts into two equal voltages of 115 each.
It will draw it's current through one of the run windings for a few seconds during starting, but that doesn't cause a problem.
All three windings are rated at 115 volts.
PS - These comments and the diagram refer to the basic general purpose motor. There are many other winding arrangements.
[This message has been edited by electric-ed (edited 11-01-2002).]