Operations Research is a much broader field than Financial Engineering, which is often considered a subdiscipline of O.R.
O.R. is also sometimes referred to as, and overlaps with, "Management Science" and "Decision Science".
You can learn more about O.R. from the website of the main professional association for that field,
http://www.informs.org/ , which markets the field as "The Science of Better" :
http://www.scienceofbetter.org/what/index.htm
http://www.scienceofbetter.org/or_executive_guide.pdf
The foremost concept in O.R. is that of optimization, which was pioneered by the late George Dantzig, who invented the Simplex Algorithm which is the key to Linear Programming.
http://en.wikipedia.org/wiki/George_Dantzig
http://en.wikipedia.org/wiki/Simplex_algorithm
At some leading universities such as Columbia, Cornell, and Princeton, the Financial Engineering program is run by Operations Research department:
http://www.ieor.columbia.edu/
http://www.orie.cornell.edu/
http://www.orfe.princeton.edu/
With a degree in O.R., you could perhaps get a job at a firm like Google, helping optimize their search functionality or figuring out how to target online advertisements (for example.) With a financial engineering degree, you would more likely obtain a job in a financial institution or in a financial software company.
The key distinction is that an O.R. degree is very broad, with lots of applications outside of finance, while an F.E. degree is much more specialized.
I hope this helps.
