Organization, administration, and maybe some fine points on doctrine. Otherwise, as long as the nondenominational churches are Christian, they are pretty similar.
History of the Methodist Church. In the 16Th Century, Martin Luther began the Protestant (based on the word "protest") reformation by breaking with the Roman Catholic Church and forming his own church which is known today as Lutherans.
Around the same time, Henry VIII wanted a divorce and the Roman Catholic Bishop of England wanted to be married, so they broke away and formed the Church of England (the Anglican Church). The Anglican Church is also considered to be Protestant but was set up to mirror the Roman Catholic Church except that it was headed by the King of England, not the Pope, and obviously divorce and clergy marriage were allowed.
An Anglican minister named John Wesley began a bible study group that became known as Methodists because of their systematic way of studying the Bible. He sent representatives to America where they rode circuits throughout the frontier and preached from make-shift pulpits.
Wesley remained an Anglican minister his entire life.
However, after the American Revolution, England broke ties in the U.S. and the Circuit Riders formed an official Methodist Church. Also, the Anglican Church in America became known as the Episcopalians.
Both Churches fall under the category of "Protestant Churches." There are many more denominations of Protestant Christian Churches that developed separately. All believe in the Gospels of Jesus Christ but many have fine points of differences in dogma.
When someone says that they are non-denominational, that means they do not subscribe to any specific church administration. They just believe as Christians on their own. It's a bit odd that someone would claim to be a member of a non-denominational church. Usually, people who form a new congregation will assign a name their new church and it will just be added to the long list of separate Protestant Churches.