Now that's a very good question. Note that the question is not just asking what are the differences between project management and operations management, but what are the fundamental differences in managing the respective work - if any. We certainly had to scratch our head a bit. It seemed to us that before jumping in and dreaming up some "fundamental differences", it is first necessary to make sure we are clear on what we mean by "projects" and by "operations" in the first place.
Of course "work" as the result of a new initiative of some sort is clearly best managed as a "project", while "work" that is being done on a routine basis and has been done like that for some time is just as clearly a part of "operations". Nevertheless, there are a surprising number of situations where the "work" can go one way or the other. That is, management can decide to manage this class of ambivalent work as a part of operations, or separate it out as a project - and manage either way accordingly.
But back to the main question, the next obvious issue is to pose the counter question: "In what context?" And to this, given the background of the owner of the original question, we assumed that the answer is in the context of the evolving and currently popular espoused disciplines of project management and operations management. So, as a starting point, we decided to rephrase the question thus: "What are the fundamental differences between managing project work (i.e. project management) and managing operations work (i.e. operations management)? Note that this is not exactly the same as the original question because this revision shifts the focus from the "work" to the "management of the work". However, this does allow us to look for the comparison from a broader perspective.
Our first reaction was to check the traditional management sources for help in this regard, especially for the respective definitions. For example, the Project Management Institute ("PMI") did a lot of work on this issue as a prelude to launching its Project Management Professional ("PMP") certification program around 1984. Unfortunately, the definitions of "project management" and "project" are multifarious and often hotly contested, and insufficiently robust for the purposes of this inquiry. Similarly, you might think that Operations Management and Business Operations would be the same thing - but apparently not, well, not quite.
So we turned to Wikipedia, the free on-line independent encyclopedia, for a public and erudite viewpoint.
4. That is to say the existing recognized project and operations management associations.
5. The original conclusions of the work done by Dr. John Adams around 1983-5 is captured in summary form in the following Issacons: Project Management Topic Levels; Why Project Management?; Special Features of Projects; and Comparing Projects & Operations.
6. For "project" see pmglossary/PMG_P09.htm#Project; for "project management" See pmglossary/PMG_P12.htm#Project Management.