The atomic mass unit (u or amu) is one unit for measuring the atomic mass of particles. It is defined as one-twelfth (1/12) of the mass of an unbonded Carbon-12. This is equal to 1.66053892 × 10-27 kilograms, making it useful for talking about the mass of individual atoms or molecules.
The value for molar mass of a substance and the atomic mass are the same number, however they represent two different values. For example, the molar mass of iron is 55.845 g/mol and the atomic mass of iron is 55.845. While the atomic number represents the mass of one particle (in this case an iron atom), the molar mass represents the mass (in grams) of one mole of these atoms.
Read more about the atomic mass unit at Dr. Rowlett's unit dictionary.