What does "level of assurance" (LoA) mean, which synonyms are in use, and which look-alike term is not a synonym?

The level of assurance states how confident a relying party can be that a subject really owns the identity it claims; it is also called trust level (Vertrauensniveau) or security level (Sicherheitsniveau), but not "level of authentication".

To make quality easy to compare, it is sorted into a small number of steps, usually three or four trust levels (Vertrauensstufen). A service then simply demands "level 3 or higher" instead of listing every technical detail.

The crucial point is what the level is about: not how strong the login mechanism alone is, but how certain the RP can be that the subject behind the login is the real holder of the identity. That certainty depends on much more than the authenticator: how well the person was identified at registration, how the authenticator was handed over, how trustworthy the operator is, and how the result is passed on.

That is exactly why "level of authentication" is not a synonym, even though it abbreviates to LoA as well. It would suggest that only the login step counts. A hardware token handed to an unverified person still gives low assurance about who that person is.

Go deeper:

• EU eID: eIDAS Levels of Assurance — the European Commission's plain-language definition: how certain a service can be that it is really you.