The many differences between Catholics and Methodists can be summed up into the influence of the church and its hierarchy and the role of the Bible. Both religions are Christian. The Methodist religion is a sect of Protestantism.
In general, Catholicism places a lot more power in the authority of the church than Protestantism. The Catholic church as a complex hierarchy with leaders who are appointed from within. Protestants elect their officials in democratic fashion. Catholicism also emphasizes the importance of the role rituals play in salvation, whereas Protestants believe that salvation is achieved only by confessing one's sins, asking for forgiveness and living life in accordance to the Bible. Protestants also interpret the Bible more literally than Catholics. Children tend to be baptized into the Catholic faith son after they are born because the Catholic belief in original sin means that everyone is born sinful and cannot enter Heaven without first being baptized. Although Christians also believe that people are inherently sinful, they believe that God makes exceptions for babies and other innocents and allows them into Heaven. So baptism in Protestant religions is usually done when individuals are old enough to profess their devotion to God. The two divisions of Christianity are also split on their visions of Heaven and Hell. Catholics believe them to be more figurative whereas Protestants think of them as literal places.