Disclaimer: the following is doomed not to be comprehensive. (I'm still cautiously optimistic about it being at least somewhat correct.)
Some OR research is devoted to theory: proving that some problem is NP-weird, finding worst case bounds on either computation time or the gap between achieved solution and optimal solution for some algorithm, and so on.
Some OR research is devoted to developing (or refining) algorithms applicable to OR problems. So people may work on things like figuring out facet defining cuts for specific combinatorial problems, or accelerating convergence of data fitting algorithms, or concocting new metaheuristics. This intersects with my "theory" category; figuring out where the boundary is is left to the reader as an exercise.
Some OR research is devoted to application. Here what makes it research (as opposed to just solving something) may be applying an OR framework to a problem not previously recognized as fitting it, or finding a non-obvious model for a problem, or finding heuristics specific to a particular problem or problem class. In some cases just identifying the problem and formulating a model may be novel enough to be considered research.
As far as current topics, (a) they vary depending on which category you're looking at and (b) to borrow from Shakespeare, there are more topics in heaven and earth than are dreamt of in my philosophy. A good way to identify current topics (give or take having any idea what the terminology means) is to look at the program of a relevant conference. INFORMS maintains a calendar of both past and future meetings. You can look for recent past conferences, drill down to the program for one, and have a look at what was presented. Fair warning: if you grab a national conference without having a pretty good idea what sorts of papers you are looking for (e.g., healthcare applications), you will drown quickly. So you might want to look at a regional or specialty conference first.
