What are the differences between the late eighteenth-century Historicism developed in Germany, and the New Historicism developed by Greenblatt?
Eighteenth-century historicism is usually associated with the Romantic movement and the writings of Leopold von Ranke. Essentially, Ranke argued that culture (especially high culture and politics at the state level, which was what he was primarily interested in) was determined to a great extent by the times in which one lived--the material, economic, and other factors that were specific to one's time and place. Culture, and more broadly human nature, were therefore not fixed or unchanging. Ranke also argued for the importance of historical facts--he was one of the first historians to engage in rigorous archival work--and he saw history as an unfolding of facts that could be understood and related by scholars.
One major difference between the two is that Stephen Greenblatt was interested first and foremost in historicizing works of literature, most famously Shakespeare. Greenblatt's field is literary criticism, and while Ranke was also interested in literature and the arts, his field of inquiry was much wider. Greenblatt, like Ranke, explains literature more in terms of historical context than, say, structuralists, who were focused more on the influence of literary forms and tropes on writing. Another difference is that von Ranke and other early German historicists still, like Hegel, understood history in terms of the works of God on earth. Ranke wrote:
In all of history God dwells, lives, can be recognized. Every deed gives testimony of Him, every moment preaches His name, but most of all, it seems to me, so does the connectedness of History...
Indeed, Ranke and his contemporaries largely saw history as a means for understanding the role played by God in the world. Greenblatt's approach is more secular, as is most twentieth and twenty-first century scholarship.