Two streams flow into Evangelicalism today according to Roger Olson in his fine new study, Reformed and Always Reforming. Here are the two streams, and they derive also from the fine studies of Mark Noll, the Dean of American Church history and evangelicalism:Pietism and Puritanism.

Many today, like John Piper in his recent statement (and I will be responding to him soon), really do think the Puritan strain is the only genuine evangelical strain and that the Pietists are Romantics or Liberals or something else (like Arminians).
Pietism adds a strong experiential dimension to classic Protestantism according to Olson (47). Pietism is inwardly focused and tends toward synergism, as seen in Arminianism. This looks back to John Wesley.
Puritanism adds a strong intellectual dimension and it tends to be publicly focused and is Reformed and Calvinistic. These folks look back to Jonathan Edwards. Here is a picture of Edwards and John Winthrop, a Puritan.

Evangelicalism arose out of both of these — it is the (Hegelian) synthesis as it were. From the start it was “full of tension” but marked by a conviction that God could transform sinners. To these two streams was added, from Protestant scholasticism, a focus on “correct doctriune and orthodoxy.”
Olson says evangelicalism is therefore an “unstable compound.”
The Puritan stream: “Typical of this strand of evangelicalism is the Alliance of Confessing Evangelicals that publishes Modern Reformation magazine. These evangelicals wince at popular revivalism, synergistic folk religion, and progressive evangelical thinkers who experiment with new ways of thinking about God, the Bible, and salvation” (49).
The Pietistic stream: They “revel in transforming experiences of God’s Spirit, Jesus-piety, and a sometimes seemingly cavalier attitude toward tradition.”
The vast bulk of evangelicalism is in between these two poles, though today we are seeing an increasingly aggressive stance taken by the Puritan stream in the Neo-Reformed movement.
What then is evangelicalism?
Mark Noll: “a large kin network of churches, voluntary societies, books and periodicals, personal networks, and emphases of beliefs and practice.”
Roger Olson: “a vast and diverse collection of individuals, churches, and groups.”
Nathan Hatch: “There is no such thing as evangelicalism.” It is too decentralized.