Unless you have access to classified material, both the US DoD/DIA designations and their NATO reporting names cannot generally be verified.
Due to the above reason, and some mentioned later below, I pretty much ignore both of them and use their domestic designation (GRAU or other Index Code) and their codename if known.
As far as I'm aware, the SA-xx bit is the US DoD/DIA (Department of Defense/Defense Intelligence Agency) designation, whilst the reporting name (codename) is in reality the NATO bit.
The designation/reporting name combinations are often so poor in their accuracy that they don't even represent a (Russian) domestic system!
Those for the S-300 family of systems are a prime example. Example problems are system families are left out, are combined, or the designation/reporting name combination is in reality assigned to an export model?
Most people are not aware of the inaccuracies and problems with verification, and boldly state this or that combination as they have seen on this or that website.