The following terms have traditional meanings for the Anglican Church, and possibly beyond:
A churchman is in principle a member of a church congregation, in practice someone in holy orders.
A clergyman can be assumed to be in holy orders. The clergy is a term applied widely across many religions, while clergyman has connotations at least of Protestantism: while a Catholic, Anglo_Catholic or Orthodox Christian. A minister might belong to any Protestant church (not Catholic).
A pastor is the senior local minister (or priest), for example in a parish.
A preacher, from the Anglican point of view, is a colloquialism used for a clergyman rather than a formal title — or it may be someone who preaches.
A canon is a priest who is specifically attached to a cathedral and has some responsibility its organisation.
I know not which is the more startlingthe début of the unfortunate clergyman, or the instantaneousness of his end.
This unfortunate clergyman may have had something in him, but I judge that he lacked the gift of seeming as if he had.
It is probable that this unregarded, young, shy clergyman, when at length he suddenly mustered courage to cut in, let his high, thin voice soar too high, insomuch that it was a kind of scream.