The two key differences between Methodist and Presbyterian beliefs are that Methodists reject the Calvinist doctrine of predestination while Presbyterians accept it and that the Methodist church is organized along traditional episcopal lines, whereas Presbyterians have their own unique system of leadership by elders (or "presbyters"). Otherwise, these two Christian denominations share many of the same qualities.
The acceptance or rejection of the Calvinist doctrine of predestination is a fundamental and far-reaching difference. In short, John Calvin's doctrine holds that only certain people are destined for salvation, while the rest are destined (or "devoted" by God) to damnation.
In other words, unlike all other major Christian denominations, Presbyterians believe that God has actively selected people to respond to his invitation of salvation.
The organization of Presbyterianism is another important difference. Elders are elected and ordained to positions of authority from the laity. Their role is then to serve the interests of their congregation as part of a governing body, or "session." When a number of sessions assemble together to discuss church affairs, they are called a "presbytery." Collectively, multiple presbyteries are referred to as a "synod." When coming together to discuss matters pertaining to the denomination at large, synods form the Presbyterian "General Assembly."