I did read Jane Auten and the Clergy - but that was a while back ;-)

I suppose Clergyman is a general catch-all term. A curate was the 'assistant' of the main holder of a living, or did the duty of the parish in their absence. As Mary Crawford said "...their curate does all the work, and the business of their life is to dine!" (Quote from memory - hope it's right!) Charles Hayter is a curate, holding a living for someone underage, and then hoping to become curate to Dr Shirley.

I'm not absolutely certain, but I think there is a difference between a vicar and a rector - I think it's to do with there being land attached to a rectory living. I may be wrong. But consider that Mr Collins is Rector (and we know about his gardens!) and Mr Elton is a Vicar, with the Vicarage being in Highbury. Mind you, he also had some gardens that his Dear Augusta thought people would like to explore! I think a Rectory possibly had a Glebe attached. Jane Auten's father certainly had a sideline in agriculture!