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 was, I think 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.
I think you really need to consult a good local history manual, medieval/early modern church law and practice were pretty complicated!
Edit The **rector* of a parish is, essentially, the owner - the one entitled to the great tithes and to appointing the priest. The rector may be the priest, but - pre-Reformation - could well be a monastery, university, prelate or other. Post-Reformation, rectors were often the largest landowner locally, or indeed some distant noble. S/he could obviously not act as priest, not being ordained, but were said to have the gift of the living - eg could appoint a vicar (priest) as a form of patronage. In the Anglican Church, lay patrons still exist, and can offer a candidate for a parish, subject to the Bishop's approval.