Pentacostal is a religious movement within Christianity that places special emphasis on the direct personal experience of God through the Baptism of the Holy Spirit, as shown in the Biblical account of the Day of Pentecost (Acts 2).
Within Pentecostalism there are two major groups, Trinitarian Pentecostals and Oneness Pentecostals. However, many Pentecostals also consider themselves part of broader Christian groups
Methodism is a movement within Protestant Christianity represented by a number of denominations and organizations. The Methodist movement traces its origin to the evangelical awakening in 18Th century Great Britain. Methodism flowed from the work of John Wesley, who was an Anglican clergyman. Thus "Methodism" is commonly taken as "Wesleyan Methodism". Wesley sought to keep Methodism as a revival movement within the Church of England, and a significant number of Anglican clergy were known as Methodists. Other 18Th century branches of Methodism include Welsh Methodists, later the Calvinistic Methodists, from the work of Howell Harris,  and the Countess of Huntingdon's Connexion through the work of George Whitefield. The influence of Lady Huntingdon and Whitefield on the Church of England was a factor in the establishing of the Free Church of England in 1844. Through vigorous missionary activity Methodism spread throughout the British Empire, the United States, and beyond.
Early Methodists were drawn from all levels of society, including aristocracy.  But the Methodist preachers took the message to laborers and criminals who tended to be left outside of organized religion at that time. Wesley himself thought it wrong to preach outside a Church building until persuaded otherwise by Whitefield.