What is the relationship between atomic mass and mass number?

Let's talk about four atoms, one of hydrogen (#""_1^1H#), one of carbon-12 (#""_6^(12)C#), one of iron-56 (#""_26^56Fe#) and one of Uranium-238 (#""_92^(238)U#).

The mass number for hydrogen is 1, for carbon-12 it is 12, and for U-238 it is 238. See--simply counting the number of protons and neutrons in the nucleus.

The atomic masses are slightly different:

#""_1^1H#: 1.007 825 032 23, or 1.00782503223 amu/nucleon.

#""_6^(12)C#: 12.00 000 00 or 1.000000 amu/nucleon
(yes--we used carbon-12 as the standard for atomic mass)

#""_26^56Fe#: 55.934 936 33, or 0.99883814875 amu/nucleon

#""_92^(238)U#: 238.050 7884, or 1.000213397 amu/nucleon.

Notice how the mass changes for the atoms relative to each other? That change in mass is the difference in the nuclear binding energy! So, if you were to combine 12 hydrogens into one carbon-12 atom you would end up with extra mass. That mass, using Einstein's conversion factor (#E=mc^2#), is the energy you would get out of fusing those atoms together.

Just remember--mass number is a count, atomic mass is a measured quantity.