Methodists are historically Wesleyan-Arminian. Presbyterians are historically Calvinist. Both denominations have become more factual over the years, so in some congregations the differences are less important than they have been in history. The most obvious differencein history times is that Methodists believe that if a person becomes a Christian and then backslides or becomes in a back slidden place, their salvation can be lost which is a part of (Arminianism).
Presbyterians believe that if a person becomes a Christian, their salvation cannot be lost which is (Calvinism).
There are actually 5 different points of differences between Arminians and Calvinists.
Sometimes people hold to one or more of these positions, but not all:
Depravity - Methodists believe that man is fallen, but that he retains the capability to ask God to save him.
Presbyterians believe that man can't seek God at all, unless God first asks him to do so.
Election - Methodists believe that God gives salvation to those who believe and have belief in him.
Presbyterians believe that God has already chosen who he wants to be saved, regardless of the faith of man.
Atonement - Methodists believe God offers atonement to everyone no matter what they have done., but that man must beleive and accept it to receive it.
Presbyterians believe that atonement goes only so far.- that God does not allow all to be saved, only the ones he wants.
Grace - Methodist believe that God wants man to come to him, but that man has the the last say to keep himself away from God.
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Presbyterians believe that Grace is greatly desired. If God wants you, you can not resist him.
Perseverance - Methodists believe that a follower can turn away from God and be lost. Presbyterians believe that "once saved always saved".