Atomic mass
One mole of a substance always contains almost exactly the "standard atomic weight" or "molar mass" of that substance; however, this may or may not be true for the "atomic mass," depending on whether or not the element exists naturally in more than one isotope. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The "atomic mass" of the Fe isotope is 55.935 u and one mole of Fe atoms would then in theory have a mass of 55.935 g, but such amounts of pure Fe have never been found (or separated out) on Earth. However, there are 22 mononuclidic elements of which essentially only a single isotope is found in nature (common examples are fluorine, sodium, aluminum and phosphorus) and for these elements the standard atomic weight and atomic mass are the same. Samples of these elements therefore may serve as reference standards for certain atomic mass values.
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).