In what ways might european empire building be understood as a single phenomenon?

It would be difficult and near impossible to see this as a single phenomenon and for it not to be seen as part of a broader process of colonization and imperialism at the time. However, one distinct feature of the colonies in North America was that there was massive migration of Europeans to these colonies whereas in other colonies at the time the migration was not as substantial. 

The Puritans did organize their New England towns and villages according to the religious beliefs. They were arranged this way because the Church of England was as a result of the political struggles.