What those titles mean (if they exist) and how they work are specific to each covenant.
A covenant may have a single leader, or they may not.
The title of that leader may be "princeps", or "disceptator", or any of a number of other titles depending on what the people writing the charter for that covenant thought was a good idea.
Such titles are not universally defined or used throughout the Order of Hermes.
Covenants list the following as possible titles for the leader of a covenant:
"
princeps (first, chief), pontifex
(high priest), imperator (commander-
in-chief), rector (guidesman, gover-
nor), aedilis (aedile), dictator, discepta-
tor (chairman), interpres (spokesman),
ductor (leader)"