Presbyterianism and Episcopalianism (sometimes known as Prelacy) are different ways of organising the church. The Reformers, especially from the time of John Knox and Andrew Melville, believed that Presbyterianism was clearly taught in the New Testament, and that to try and organise the church a different way would be wrong. The Church of Ireland and the Church of England are examples of Episcopal churches today.
In Presbyterianism, Jesus Christ is the head of the church. Each congregation elects elders who meet together as a session to make decisions about the congregation. A minister is an elder with a special responsibility for teaching and preaching. A minister and elder from each congregation in a certain area also meet together as a Presbytery every few months to make decisions about the churches in that area. Once a year, a minister and elder from each congregation meet as a Synod or (if the church is very big) a General Assembly to make decisions on the church in the whole country.
In Episcopalianism, the King or Queen is usually seen as head of the church. The church is ruled by Archbishops and Bishops. Most of the kings during the Reformation and Covenanter period preferred Episcopalianism because it was easier for them to control. They would only have to try and influence the Archbishops and Bishops, rather than each individual elder and minister. At the Reformation, many Episcopalians still tried to spread the teaching of the Reformers though and in England John Knox worked alongside Archbishop Cranmer. However he refused the offer to become a bishop.
DSCHT: Episcopalianism, Presbyterianism