One use was preferred in Europe, one in America, but the term was so rare and the historiographic problem so minor that we have now forgotten which was which. However, a similar problem arises in many of our conversations these days, and it is one which scholars ought to get busy building into their glossaries.
Here in Europe -- specifically, here in Romania -- the term Neo-Protestant is used, both by scholars and by other educated people, as a catchall for those religious communities which emerged after the Reformation, but from within the ideological world created by Protestantism. So, for example, the Lutheran, Reformed and Anglican churches are Protestant, while Baptists, Pentecostals, Adventists are Neo-Protestant. (Meanwhile, coeval movements within the Orthodox and Roman Catholic realms, such as the emergence of the Byzantine-rite churches or the Lord's Army, are classified differently).
This is an extremely useful distinction, at least on par with the one between the "magisterial" and "radical" Reformations. It may require some clarification, particularly with regard to Anabaptists and Methodists, but it is useful.
(In particular, this distinction -- were it to become common in Anglo-American circles -- could put paid to the anomalous refusal of some Anglicans and Lutherans to identify themselves as Protestant. Since the time of that very Romantic revival mentioned above, many of us have pointed in dismay to, say, Baptists, Quakers and Adventists, saying in effect, "Neither our theology nor our worship is as much like theirs as it is like the Pope's; so if they are Protestants, then we must be ... something else." Obviously, we at the Egg participate in this little charade, but we do so more from necessity than from joy. And if they are Neo-Protestants, then we can reclaim our proper Reformation identity without much fuss.)
There is, however, a problem. In Anglo-American scholarship, the term Neo-Protestant already has two senses. It is used both to describe (1) the modernizing, "liberal" movement which followed after Schliermacher (so, for example, the Blackwell Encyclopedia of Modern Christian Thought), and also (2) the eventual reconsideration of "classical" liberalism in the works of Barth & Co.
This latter usage is fairly rare; the preferred term is Neo-Orthodox, which from our current perspective is fraught with confusion of its own. (Oy, vey.) Still, it is common enough. Two minutes on Google turn up numerous examples, including some from notable theologians and sociologists. Part of the confusion is that a theological position opposed to "modernism" in any form makes no real distinction between Tillich and Barth. (So, for instance, Carl Henry, in this 1969 essay.)
Still, neither of the two conventional Anglo-American uses of "Neo-Protestant" is particularly widespread, nor does either one define a semantic boundary in such urgent need of definition as the Central European use. Historians, social scientists and pastors all have a pressing need for some easy way to distinguish the churches which emerged during the Reformation proper from those which in subsequent generations built upon, or strayed from, its legacy.
So let's hear it for neo-Protestantism! Hooray!**
* And, by the way, don't bother consulting Wikipedia on this. The relevant articles don't acknowledge the double-sense, and in any case are full of Missourian disinformation.
**This cheer is directed only to the technical term, and not to the movement identified thereby. Lest you think we were changing horses in midstream.