In 1609, John Smyth led a group of separatists to the Netherlands to start the General Baptist church with an Arminian theology. In 1616, Henry Jacob led a group of Puritans in England with a Calvinist theology to form a congregational church that would eventually become the Particular Baptists in 1638 under John Spilsbury. Both groups had members who sailed to America as pilgrims to avoid religious persecution in England and Europe and who started Baptist churches in the early colonies. The Particular and General Baptists would disagree over Arminianism and Calvinism until the formation of the Baptist Union of Great Britain in the 1800s under Andrew Fuller and William Carey for the purpose of missions. American Baptists soon followed suit.This is the Separatist view of Baptist history. Most informed Baptists believe this. The competing Landmark and Anabaptist views of Baptist history is not credible outside certain circles.
According to this Baptist website, it's pretty accurate to call Baptists Protestants: