@ElizaBennett - Love your screen name! I hope you are living happily ever after with your own Mr. Darcy.
I have a nice annotated edition of the novels--birthday present from my husband--that explains some of those things one always wondered about (like how a phaeton is different from a barouche).
Apparently, in the old Church of England, people were obligated to pay tithes to support their minister. Getting a permanent, supported post like that was called getting a "living." The only difference between a vicarage and a rectory, by definition, had something to do with the precise nature of the living and how the guy was supported.
A curate, on the other hand, was a clergyman with no living of his own who was paid for a wealthier minister to do his preaching for him. This would be the cause with a minister who had multiple livings and couldn't physically be at all of them; he would hire a curate to help him out. I think the Brontes' father was a curate and Jane Austen's father was a vicar, though obviously not a terribly wealthy one.