A Baptist is basically a member of a Christian Domination. A Baptist is characterized by rejection of infant baptism. They are in favor of believer's baptism by immersion. Baptism emerged from the English Dissenter or Non-conformism movement of the 16th century. They are usually called as Protestants
On the other hand, Methodists are those Christians that follow Methodism or Protestant Christianity. They are characterized by their view of free will through God's prevenient grace. This sect of Christianity emerged from the Reformation of Church movement.
I could answer with a joke: Well, a Methodist will wave to you if they see you in a liquor store. Or, with a more "factual" theological answer which relates to the state of grace. The previous responder's noting the doctrine of free will is very important. Often, at least Southern Baptists will say "Once you're saved; you're always saved." There can be no fall from grace if the grace is "genuine." Methodists, on the other hand, believe that even if you're in a state of grace, because of free will, you can choose to do such evil that would make you "fall" from grace - from which state you can recover again, if you were truly repentant. And, because of free will, Methodists differ from Calvinists (i.e., mainly Presbyterians) over the concept of predestination.