I’ll try my ever so poor attempt, since no-one else has chimed in. I may be all wrong though.
As I understand it, priests from Aaron, were priests for life, and each first born son was priest, or perhaps it was the father was automatically the priest in the family. Basically, it wasn’t restricted to a single Tribe as it was after the Levites stepped up and slew all the idolators.
The Levites, as I understand it, were the priests to serve in the sin offering, served for only a short period of time (there were specifically defined age limits) and their position as priest was determined by their birth order.
I believe the priests of the Order of Melchesadec was not responsible for a sin offering as much as a love offering and didn’t offer animal sacrifice, but rather an offering of bread and wine, the foreshadowing of the Eucharist. I may have the duration of the priests of the Order of Aaron confused with these of Melchesadec.
Good question. I look forward to the answers offered by those more knowledgeable.
God Bless,
CARose