In small theaters, the two jobs often overlap. The job of the production manager is basically administrative, while that of the stage manager is essentially hands on.

The production manager generally is responsible for budgeting, scheduling work, and coordinating the various production departments. Stage managers typically provide practical and organizational support to the director, actors, designers, stage crew and technicians throughout the production process. They also are the director's representative during performances, making sure that the production runs smoothly.
http://www.aact.org



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Note added at 5 days (2015-12-02 15:06:03 GMT)
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In no Theater Arts program have I ever seen /How to Keep a Play Running/ listed as a course.