Atomic mass
The atomic mass ("m") is the mass of an atom. Its unit is the unified atomic mass units ("abbr." u) where 1 unified atomic mass unit is defined as of the mass of a single carbon-12 atom, at rest. For atoms, the protons and neutrons of the nucleus account for nearly all of the total mass, and the atomic mass measured in u has nearly the same value as the mass number.
Milli mass unit
Since 1961 the unified atomic mass unit "u" has been defined as 1/12 the mass of C. Before that the atomic mass unit "amu" was defined as 1/16 the mass of O (physics) and as 1/16 the mass of O (chemistry). Thus the publication date in literature ought to be heeded when reading about the milli mass unit as its name does not reveal whether it refers to the old amu or the newer u.