I won't try to give an answer about which word to use, because nature has no respect for our words. Instead, let's look at what we know about nature.
In all descriptions of patches of space-time small enough to be described by Special Relativity (or sometimes even by Newtonian physics) all known experiments are consistent with the conservation of energy. Furthermore, our basic framework for describing how the world works (quantum mechanics) has conservation of energy emerge as an exact property from the structure of the theory. So we believe that conservation of energy is exact within this domain.
Extension of this conservation rule to broader domains, in which General Relativity is required to describe space-time, is somewhat more complicated. The problem is that there is no clear unique way to take multiple fixed-time slices and compare the energy in them, because there are so many choices of different space-time coordinates. I've heard that, with some care, a law like energy conservation can be constructed for this more general case.
If some supplement turns out to be needed to the basic structure of quantum mechanics, then it may turn out that energy conservation is not exactly right. Some such ideas have been proposed, but there is no evidence for them.
(published on 08/14/08)