Canonical Orders

Every Bishop or Priest who has a "church" has what is known as a Canonical Order.

A Canonical order is just the supporting cast of Deacons/Priests who assist the Bishop in the diocese. The type of Priest who might have a Canonical order would be a parson, or a provost.

Once a Friar achieves the rank of Priest, he or she may either remain in the Order, or they may join one of these Canonical orders. Given the nature of our little set up here, Friars will generally end up working for their Bishops, or a Priest within their county/shire.
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In real-life, Friars generally don't aspire to be Priests. There are a few who do become Priests, but this is not why they join an Order. Those looking to be Priests generally join a seminary.

The only thing I can think to compare this to is enlisting in the military, and then going through OTS to become an officer as compared to going through OTS directly.

Both becoming a friar and becoming a deacon involve taking an exam. The friar's exam is considerably easier and is the only one open to villeins, but being a friar and being a priest are even in Hyperion two different kinds of commitments.

For now, those taking the priest exam can become priests, but this is only because we need people to fulfill the roles of the first priests. Later, the exam will only allow you to become a deacon - acquisition of holy powers and the ability to demonstrate them is the second part of becoming a priest.

The roles of a priest and a friar are very different, however, both have appeal. Priests generally occupy different roles on the battlefield than friars, who after all may still be normal enlisted footmen in the military. Priests also are the ones who are in charge of churches, even if they are alone in their village church - whereas a friar is always guaranteed a community. Even a noble knight who wishes to join the clergy may elect to join as a friar rather than becoming ordained as a priest, so even though a friar is ranked lower in the church heirarchy than a priest, it really amounts to the type of playstyle you desire.

This doesn't mean Priesthood is closed off to Friars, once they've fufilled the requirements, it just encourages members to stay in various Orders.

Orders themselves generally have their own hierarchy as well. This is more apparent in Military Orders, where Sgt-brothers are ranked below Knight-brothers, which are all under the Grandmaster.

To say a Friar is a "lower rank" then a Priest is again comparable to enlisted vs officers in the military. What does socially inferior really mean anyway? Can't attend cocktail parties?