Atomic mass
The atomic mass of an element is the microscopic mass of an element in atomic mass units.[1]
This means that different isotopes of an element have different atomic masses (for example 235U has a different atomic mass than 238U).
The atomic number, also known as the average mass, or atomic weight, is an average mass of a distribution of isotopes of the element. Because it is an approximation of this mass, it is roughly the sum of the number of protons and neutrons in an atomic nucleus.[1]
Careful measurements of the mass of individual atoms will yield an atomic mass. To learn more about atomic mass, and its units, check out hyperphysics or UC Davis' Chem Wiki.