Religious orders are generally divided by their devotion to the individual deities.
Aiding religious orders will allow the player(s) to advance along the renown ranks of that order. It is worth noting that clerics who belong to an order are automatically awarded the requisite points to bring them into the 2nd, 3rd & 4th levels as they advance in clerical class levels. You typically do not advance using favors because devotion to the gods is expected, however, good works are rewarded. Regardless of where they came from in society these individuals are now members of then Orderborne community.
- Levels 1-2 Cleric = Acolyte or Cultores
- Levels 3-6 Cleric = Brother (Mars dancers are called Salii and expected to perform at holidays)
- Levels 7+ Cleric = Arvales/Flamines/Sodales/Vestals (if virgins) - All generally referred to as Priests.
- Augeres - Priests who interprets the will of the gods
- Pontifex Maximux - the supreme leader of all the priests.
Above 7th level it's a political office and not one an adventurer can expect to hold. It's difficult to be political when you are absent.
You may remember there is more written about the details of these religions here.