The Protestant Reformation in the 16th century can be broadly divided into roughly three types of reformation.
In the first, there were the Magisterial Reformers, this is the term we use to describe Martin Luther, John Calvin, Ulrich Zwingli, etc. It refers to those who, more-or-less sought for reform within the already established church structures as they already existed.
The Magisteral Reformation can itself be split into two camps: Lutheran and Reformed. The Reformed Tradition refers to the reformation work of John Calvin and Ulrich Zwingli (as well as John Knox and others). Whereas the Lutheran tradition is seen in, well, Lutheranism. Both Lutherans and Reformed agreed (and still agree) on many very important points. For example, the chief doctrine of the Reformation was that we are justified by grace alone through faith on Christ's account alone. This was Luther's rallying cry, which Calvin and the Reformed leaders also took as their own.
In the second, there was the English Reformation, which refers to when King Henry VIII broke ties with the Pope in order to establish an independent English Church, with himself as temporal head--basically because he wanted to divorce his wife and marry another woman, and the Pope said no. This began a period of turmoil in English Christianity between Protestant-friendly factions and anti-Protestant factions. Henry himself was anti-Protestant, which is also why he had William Tyndale put to death; of course Henry's successors would be more pro-Protestant and would, instead, have Catholics put to death. Eventually the Church of England would undergo further Protestant reform, largely influenced by the Reformed tradition. And high-church, catholic revival movements such as the Oxford Movement would also lead some Anglicans toward a more Catholic expression of Anglicanism in later centuries--giving us the modern Anglican Communion, including the Episcopal Church in the USA (Anglicanism was renamed Episcopalianism in the United States after the American War for Independence).
And thirdly there is what is called the Radical Reformation, which is largely a catch-all term referring to numerous individuals, groups, and movements that arose that were entirely outside the usual church structures. Many of these groups viewed themselves as restoring original, primitive Christianity, and turned to teaching old, long since rejected heresies, such as Adoptionism and Arianism. Some groups were apocalyptic cults, some literally used military force to occupy cities, and inciting violent peasant uprisings, which resulted in massive destruction of churches. Even in Wittenberg, Luther's home, while he was hiding, his old friend Andread Karlstadt tried to incite revolution and rebellion, having crosses and crucifixes burned, holy images were destroyed---until Luther returned and put a stop to that. Some of these groups were simple Anabaptist pacifists, like the Mennonites.
As for how Reformed differs from Evangelical, that is a larger topic:
The word "Evangelical" has been used to mean different things over the centuries. The first to use the term "Evangelical" to describe themselves were the Lutherans. Lutherans didn't call themselves "Lutheran", they called themselves "Evangelical". That term "Evangelical" was also used by Reformed Protestants as well. As such "Evangelical" effectively just became the term for "Protestant" in Germany. In fact, even today, the common word in German for Lutherans and Reformed Protestants is "Evangelische", and hence even today the largest Protestant denomination in Germany is the Evangelische Kirche in Deutchland (Evangelical Church in Germany).
In America and Britain, "Evangelical" was then applied to Protestant revivalism in the First Great Awakening, such as the sort of work being done by John Wesley, George Whitefield, Jonathan Edwards, etc. Jonathan Edwards was himself very Reformed, George Whitefield was a Calvinist Methodist, while John Wesley was an Arminian Methodist.
A word about Arminianism: In the 17th century in the Dutch Reformed Church, a controversy arose from the teachings of a Reformed theologian, Jacob Arminius, and his students who were known as the Remonstrants. They believed that there were problems in the Calvinist orthodoxy prevailent at the time, and proposed Five Points of Remonstrance. Orthodox Calvinists countered the Five Points of Remonstrance with their own five points, which came to be known as the Five Points of Calvinism, or the accrostic TULIP. In this sense, while Calvinism and Arminianism are very different theological positions on several key topics, both are part of the same Reformed Tradition.
Finally, the modern use of Evangelical has come to be used to describe the Neo-Evangelical movement that emerged in the early-to-mid 20th century. Modern [Neo-]Evangelicalism emerged largely as a response to the cultural isolation of Fundamentalism. Fundamentalism had began at the turn of the 20th century as itself a response to the Modernist controversy of the late 19th century. Theological schools in parts of Europe, mostly in Germany, were embracing certain Enlightenement ideas, and these were influencing the seminaries and theology schools. When these ideas traveled across the Atlantic, and began to appear in American theology schools and seminaries, more theologically conservative/traditional Protestants sought to affirm what they saw as biblical and Christian fundamentals of faith, and thus they began to be called Fundamentalists. The early Fundamentalists actively engaged with the wider culture, but over several decades would largely retreat from the wider culture, retreating from academia, and the like. In response to this isolationism, some chose instead to actively engage the culture, and this would give birth to the Neo-Evangelical Movement.
Arguably the most important person in the rise of Neo-Evangelicalism was Billy Graham. It was Neo-Evangelicalism because it was seen as a revival of the older Evangelicalism of the Evangelical revivalism of preceding centuries. But where the 19th century Revivalists would have tent meetings, Billy Graham was able to fill stadiums.
So, today, in the 21st century the term "Evangelical" is largely a term to refer to the Neo-Evangelical movement.
Also, Evangelical and Reformed are not mutually exclusive categories. There are many Reformed Evangelicals: Evangelicals who subscribe to Reformed theology.
-CryptoLutheran
