I work as an Operations Manager, and was degreed as an IE. My title within the company is "Plant Manager", but my work closely follows an Production/Operations Management responsibility.
I would suggest that many times the two titles mean the same thing. The Ops Mgmt types never "leave after putting in 8-8.5 hours", because the issues and problems they face confront them at all hours of the night, on the weekends, and during otherwise significantly distracting events. No IE ever had to worry about what he's going to do if his best machine operator ever quit!
With typical engineering arrogance aside, I would say that an IE that sucessfully acknoledges and manipulates the culture, environment, and operations variables will be more impactful in his pursuits than a rigidly systematic or academically constrained IE.
My perception, in the most simple definitions:
Operations Management = "soft" variables engineering
Industrial Engineering = "hard" variables engineering