In the thread that led to this one, Exapno Mapcase linked to an earlier thread . In it, MikeS made the following post, which I think is worth reposting here (bolding added).
A closed system has some total energy E[sub]t[/sub] (kinetic energy, potential rest energy, and otherwise) and total momentum p[sub]t[/sub]. No matter what happens inside this closed system, its energy and momentum will always be the same. We can define the “mass” of this closed system by m[sup]2[/sup]c[sup]4[/sup] = E[sub]t[/sub][sup]2[/sup] - p[sub]t[/sub][sup]2[/sup] c[sup]2[/sup], and since the total energy and momentum of the system can’t change, then the mass defined thusly will always be the same as well.
However, what’s not true is that the mass of a “system” consisting of two objects equals the sum of the masses of each object considered separately. So a uranium-235 nucleus at rest has a given mass; when it fissions into a krypton nucleus and a barium nucleus, the momenta and energies of the two daughter nuclei will add up in such a way that the mass of the system (as defined above) will be the same as that of the original uranium nucleus. What’s not true, however, is that the mass of the krypton nucleus (as defined above) plus the mass of the barium nucleus (as defined above) will equal the original mass of the uranium nucleus. In this sense, mass not conserved.
The bold sentence is important to understand, and why it’s important to be explicit what is being referred to when the word “mass” is used when there’s the possibility of confusion.