Chemical element
Whereas the mass number simply counts the total number of neutrons and protons and is thus a natural (or whole) number, the atomic mass of a single atom is a real number giving the mass of a particular isotope (or "nuclide") of the element, expressed in atomic mass units (symbol: u). In general, the mass number of a given nuclide differs in value slightly from its atomic mass, since the mass of each proton and neutron is not exactly 1 u; since the electrons contribute a lesser share to the atomic mass as neutron number exceeds proton number; and (finally) because of the nuclear binding energy. For example, the atomic mass of chlorine-35 to five significant digits is 34.969 u and that of chlorine-37 is 36.966 u. However, the atomic mass in u of each isotope is quite close to its simple mass number (always within 1%). The only isotope whose atomic mass is exactly a natural number is C, which by definition has a mass of exactly 12 because u is defined as 1/12 of the mass of a free neutral carbon-12 atom in the ground state.
Nuclear binding energy
Nuclear binding energy is the "minimum" energy that would be required to disassemble the nucleus of an atom into its component parts. These component parts are neutrons and protons, which are collectively called nucleons. The binding is always a positive number, as we need to spend energy in moving these nucleons, attracted to each other by the strong nuclear force, away from each other. The mass of an atomic nucleus is less than the sum of the individual masses of the free protons and neutrons, according to Einstein's equation E=mc. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.