Methodism's polity is its own invention and does not fit the usual three-way division neatly.
The organising word is connexion. Methodist congregations are not free-standing societies; they belong to a network in which ministers are members of the conference rather than employees of a congregation, and they are appointed to a place, not called by it. That appointment system, the descendant of Wesley's circuit riders, means a Methodist minister can be moved, and it is why Methodism could plant churches across the American frontier faster than any tradition that required a congregation to find and pay its own pastor.
Above the local church sit the district or circuit, the annual conference, and in most bodies a general conference that meets every few years and holds legislative authority. In American Methodism the annual conference is the basic body of the church and ministers hold their membership in it. Bishops exist in the United Methodist Church and its relatives, but the office is deliberately defined as superintendency, oversight and appointment, rather than as a claim to apostolic succession, and bishops are elected by the church rather than received from anywhere.
British Methodism went the other way and has no bishops, being governed by its Conference with a President elected annually. Both arrangements descend from Wesley, who had strong views about oversight and none at all about the necessity of the historic episcopate.
The doctrinal standards are Wesley's sermons and his Notes on the New Testament, plus the Articles of Religion he abridged from the Anglican thirty-nine. This is a tradition that codified a method and a discipline far more thoroughly than it codified a systematic theology.