AE 1981 777

[Robert Vermaat]

It's a weird term, because it seems to refer to some sort of higher rank than Centurion, or a High Ranking Centurion in the Limitanei Garrisons. In the Comitatenses and Palatina though, it seems to just mean "Centurion" generally.

Interesting, that could mean, that the Limitanei had 2 ranks of centurions like the early legions. The higher ranked were primi ordines or now called ordinarius. You could also guess, that after a few hundred years and citizen rights for everybody, the centurio princeps of an auxilia, which was the highest centurio of an auxila and 2nd in command behind the tribune/praefect was called ordinarius, too.
Due to the fact that comitatenses are always of higher rank than limitanei, every centurio of the comitatenses was an ordinarius. So in this case ordinarius is not a rank but a rank-group. Like in modern armies lieutenants are a rank group of more than on rank (1st Lt., 2nd Lt. , ...).

Possible but not necessarily so. Ranks are an odd thing, and we are by no means always certain if we are dealing with actual ranks, or maybe with grades, posts or titles, based on tasks, seniority or simply pay differences. Centurions are found in (old-style) limitanei units, ordinarii are found in (new-style) comitatenses and auxilia palatini units. At some points limitanei units become pseudo-comitatenses, still lower in rank but I doubt this transition to the field army had any implication for the names of the NCOs.