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.
Chemical element
The mass number of an element, "A", is the number of nucleons (protons and neutrons) in the atomic nucleus. Different isotopes of a given element are distinguished by their mass numbers, which are conventionally written as a superscript on the left hand side of the atomic symbol (e.g. U). The mass number is always a whole number and has units of "nucleons". For example, magnesium-24 (24 is the mass number) is an atom with 24 nucleons (12 protons and 12 neutrons).