Atomic mass
The term "atomic weight" is being phased out slowly and being replaced by "relative atomic mass", in most current usage. This shift in nomenclature reaches back to the 1960s and has been the source of much debate in the scientific community, which was triggered by the adoption of the unified atomic mass unit and the realization that weight was in some ways an inappropriate term. The argument for keeping the term "atomic weight" was primarily that it was a well understood term to those in the field, that the term "atomic mass" was already in use (as it is currently defined) and that the term "relative atomic mass" might be easily confused with "relative isotopic mass" (the mass of a single atom of a given nuclide, expressed dimensionlessly relative to 1/12 of the mass of carbon-12; see section above).
Atomic mass unit
The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, many sources still use the term "amu" but now define it in the same way as u (i.e., based on carbon-12). In this sense, most uses of the terms "atomic mass units" and "amu", today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon-12 vs. oxygen-16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.