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.
Atomic mass
In the case of many elements that have one naturally occurring isotope (mononuclidic elements) or one dominant isotope, the actual numerical similarity/difference between the atomic mass of the most common isotope, and the (standard) relative atomic mass or (standard) atomic weight can be small or even nil, and does not affect most bulk calculations. However, such an error can exist and even be important when considering individual atoms for elements that are not mononuclidic.