The naming convention seems to be roman numerals stuck on all the different variants for a lv99 staff of a particular element. For instance, the "cure staff" is called Arka IV. I believe the one for "light damage" is Arka I, the one for "light accuracy" is probably Arka II, and so on.
In other words, yes, they're probably differently named.
Also, staves are the only weapons I know of (so far) to receive this treatment. They definitely learned their lesson from the whole Teiwaz fiasco.
Edited, Jan 5th 2012 4:05am by Fynlar