Atomic mass
The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually "about" the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.
Mass (mass spectrometry)
The nominal mass for an element is the mass number of its most abundant naturally occurring stable isotope, and for an ion or molecule, the nominal mass is the sum of the nominal masses of the constituent atoms. Isotope abundances are tabulated by IUPAC: for example carbon has two stable isotopes C at 98.9% natural abundance and C at 1.1% natural abundance, thus the nominal mass of carbon is 12. The nominal mass is not always the lowest mass number, for example iron has isotopes Fe, Fe, Fe, and Fe with abundances 6%, 92%, 10%, and 2%, respectively, and a nominal mass of 56. For a molecule, the nominal mass is obtained by summing the nominal masses of the constituent elements, for example water has two hydrogen atoms with nominal mass 1 and one oxygen atom with nominal mass 16, therefore the nominal mass of HO is 18.