There are many terms for the head of a local church, and the exact differences blur over time. Often the choice is based on some theological position of the founder; a distinction that is often lost in the general homogenization of ecumenicalism.
Nonetheless, in terms of a theological position, a vicar is someone who stands in place of Christ. A person who represents Christ, the real head of the church, at the church. He has a special spiritual position and role.
A pastor is specifically someone concerned with pastoral work, that is someone who heals the wounds and broken hearts. This is frequently used in churches where the leader doesn't necessarily have a special spiritual position, he is a teaching elder, or just a selected congregant. In the UK and outside the US this person is often called a minister, which has essentially the same meaning.
A priest is much the same as a vicar, except that a priest often has the role of offering a sacrifice, which is why you see it in Catholic churches, which offer the Eucharist, the re-sacrifice of the body of Christ.
These names are often reflected in the three basic categories of church:
Episcopal, which is a church with a hierarchy of spiritual leadership such as the Church of England or the Roman Catholic church. They usually use either priest, or vicar. (And also various higher level titles like Bishop, Cardinal, Monseigneur etc.) The name derives from the Greek work episcopos, which literally means overseer, or, more conventionally bishop.
Presbyterian, which is a church ruled by elders with a central congregation of elders from each church that, democratically, set church doctrine. Examples of this would be the Baptists, the Church of Scotland, or the Methodists. They tend to use words like pastor, minister or often just elder or teaching elder. This name derives from the Greek word presbyter meaning elder, the literal meaning being that everyone is the same but the wiser older ones set the standards.
Congregational, which is largely like the Presbyterian, except that there is not ruling body of doctrine set by the churches as a group. Each church is responsible for its own. There are lots of little churches like this, and some larger ones. They often have an overall organization, but it has limited governing powers.