Upvote:5
I'm no expert, but will attempt a partial answer - first, the educational qualifications refer to:-
BA - Bachelor of Arts
MA - Master of Arts (traditionally awarded automatically to Oxford graduates one year after graduating)
BD - Bachelor of Divinity
AM - I think another description on of MA.
A clerk would probably refer to a clerk in holy orders - there were many grades of holy orders, most men at Oxford or Cambridge would be in minor orders.
A priest is a generic term for a man (prior to modern times) who had been ordained priest by a Bishop. Only a priest could absolve sins, or consecrate the bread and wine at Mass.
A subdeacon is the lowest form of holy orders, originally to assist the deacon and serve at Mass.
A rector is somewhat different. Parish priests were entitled to tithes - one tenth of the parish produce. These were divided into greater and lesser tithes - a rector received the greater tithes and was effectively the owner of the living. (A vicar was appointed by a rector and, I think, received only the lesser tithes or a stipend.)
A capellanus is a chaplain - either employed by a great family or paid to say Masses, for example, for the souls of the dead.
Edit I think you really need to consult a good local history manual, medieval/early modern church law and practice were pretty complicated!