The Church of England has many peculiarities and understanding the jargon.

What is the difference between a Rector and a Vicar?
Does a Rector always live in a Rectory?
What is a Benefice, Incumbent, Patron etc?

The difference between Rector and Vicar is largely historical.

England is divided up into ecclesiastical parishes. A Bishop is expected to ensure that someone is appointed to care for the spiritual needs of the people of each parish. This spiritual care is known as the cure of souls and originally the person given the cure was called the Curate. Today the name Curate is usually used of someone who is a trainee clergyman but in the 1662 Book of Common Prayer there is reference to Bishops and Curates which means all the clergy.

A parish can have more than one Church in which case one will be the Parish Church and the other(s) most likely will be District Churches. There can also be places of worship which might not be thought of as Churches.

In the past each parish would have been identified with a Benefice.
A Benefice is an ecclesiastical office which, under Canon law, carries certain duties and conditions (called the spiritualities) together with certain revenues (called the temporalities).
The office holder is known as the Incumbent.

Today there can be many parishes linked in one Benefice.

Historically parochial benefices were of three kinds:

• Rectories
• Vicarage
• Perpetual Curacies

In the days when Tithes were paid in England someone was entitled to receive the Tithe.

A Rectory was a benefice in which the Tithe was paid to the Incumbent. The Incumbent was know as the Rector and the Benefice house, where he lived, was also known as the Rectory.
Technically a Rector is an Incumbent whose 'tithes are not impropriate'.

In Medieval times many Benefices were owned by Monasteries. The Monstery was entitled to receive the temporalities (ie the Tithes etc) but they also had to assume the spiritualities (the spiritual care of the parishes). The Monastery would use part of the Tithe (typically a third) to pay for someone act on their behalf (vicariously) and such a person was known as a Vicar. Their place of residence became known as a Vicarage.

When Henry VIII dissolved the Monasteries their Benefices were often passed to local landowners who became known as lay rectors.

In practice today, apart from the names, the only difference is that the freehold, though not the legal possession, of the Chancel belongs to the Rector rather than the Vicar. (The Chancel is the main part of a Church building). There was a court case not long ago where a Lay Rector, who became such when they bought some land, did not wish to be responsible to repairs to the chancel.

Perpetual Curacies are a further complicated peculiarity but fairly rare.

Historically the Patron of a Church would have been the person on whose land, or in whose estate, the Church was built. The Patron reserved the right to appoint the Incumbent subject to the approval of the Bishop. Patronage is a property right and it used to be possible to buy and sell it. Every parish has a patron, sometimes a private individual or group of individuals. The Crown has substantial patronage, some delegated to the Lord Chancellor, there are a number of patronage bodies, Bishops and some Cathedrals also hold patronage and there are many other possibilities.
Today it is the duty of the Patron to find and present someone to be the Incumbent of a Parish. However, the parish appoints two representatives who act on their behalf and they are free to accept or decline any person presented. The Bishop must also agree to Induct and Institute the new Incumbent. Therefore the different parties usually work closely together through the process.

Two things mess all this up today.

1) There are now many Team Ministries where several clergy work together in several churches. The Team will have a Team Rector (the boss) and one or more Team Vicars or Team Curates. In this case the titles Rector and Vicar do not relate to the historic offices. There is no particular reason why a Team Rector should live in a Rectory.

2) In many instances the Benefice may be in suspension. This is done when there are thought to be reasons why there might be changes to the Benefice. It is not necessary to suspend it but if not the Incumbent can block any change if they so choose. With the declining number of parish clergy in the Church of England there are now many Benefices that are suspended as soon as they become vacant.
The Bishop assumes the spiritualites and temporalities and appoints someone to conduct these on his behalf whilst under suspension. The person appointed is called a Priest-in-Charge, they are not the incumbent.
Because the Benefice is suspended the Patrons rights are also suspended and likewise the Parish. This means that in theory a Bishop can impose a Priest-in-Charge although they are expected to consult with both parish and patron.

Clergy houses are collectively known as parsonages but will normally be known as The Rectory or The Vicarage usually based on the historic status of the Benefice. It would be possible today to have a new name, perhaps The Victory, although in many cases a more appropriate name would be the Recage.