Atomic mass
The atomic mass and relative isotopic mass are sometimes confused, or incorrectly used, as synonyms of standard atomic weight (also known as atomic weight) and the standard atomic weight (a particular variety of atomic weight, in the sense that is a standardized atomic weight). However, as noted in the introduction, atomic weight and standard atomic weight represent terms for (abundance-weighted) averages of atomic masses in elemental samples, not for single nuclides. As such, atomic weight and standard atomic weight often differ numerically from relative isotopic mass and atomic mass, and they can also have different units than atomic mass when this quantity is not expressed in unified atomic mass units (see the linked article for atomic weight).
Nuclear binding energy
As seen above in the example of deuterium, nuclear binding energies are large enough that they may be easily measured as fractional mass deficits, according to the equivalence of mass and energy. The atomic binding energy is simply the amount of energy (and mass) released, when a collection of free nucleons are joined together to form a nucleus.