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.
Mass in special relativity
The term "mass" in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. The "invariant mass" is another name for the "rest mass" of single particles. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Thus, invariant mass is a natural unit of mass used for systems which are being viewed from their center of momentum frame (COM frame), as when any closed system (for example a bottle of hot gas) is weighed, which requires that the measurement be taken in the center of momentum frame where the system has no net momentum. Under such circumstances the invariant mass is equal to the relativistic mass (discussed below), which is the total energy of the system divided by "c" (the speed of light squared).