I suppose I could give it a shot...

I'm not sure if there's a difference between Marxian and Marxist historiography, but Marxist is the term I've heard most often and that I'm most familiar with, so I'll try to explain that.

First, it is important to note that Marxist historiography is not synonymous with Marxism itself--you don't necessarily have to believe in all Karl Marx's theories of social development, or be a Communist yourself, to write works of "Marxist" history. Indeed, many prominent Marxist historians, such as E.P. Thompson, actually split from the Communist party for a variety of reasons. (1) Marxist historiography rather refers more generally to methods of analysis, selection of evidence, and interpretation. Georg G. Iggers wrote well on this in "Historiography in the Twentieth Century: From Scientific Objectivity to the Postmodern Challenge". Allow me to quote him:

"But official Marxist theory, despite its rigidity and sterility, could raise questions that were productive for social history. We have already mentioned the interest historians in the Soviet Bloc showed in questions of material culture...in their determination to proceed from an economic and social base to aspects of culture, food, fasions, etc., these studies resembled the search for the histoire totale of a region by Annales historians...Marxist interpretations representated a challenge to non-Marxist historiography less on political grounds than because they questioned a traditional event - and person oriented history and called for greater attention to social context and social change." (1)

It seems your association of Marxist historiography with social history more generally is not at all misguided. Though people may and certainly do disagree with Marx and Engel's views on historical causation, teleology, and so on, these philosophers raised questions that left a tremendous impact on social history. Rather than focusing primarily on "great men" and particular events (such as big battles or massacres), Marx focused on the formation of socioeconomic classes and the relationships between them, the material conditions of these classes, and how all of this changed over time.

All those are elements of Marxist historiography, but as you note, have largely been accommodated into more general social history as well. There us yet still some distinction left to Marxist history, though. As Anna Greene and Kathleen Troupe warn in Houses of History, "to conflate the broad body of social history with the work of Marxist historians may be to miss the very clear distinction between them. Harvey Kaye emphasizes the point that the British Marxist historians represent a 'theoretical tradition', the defining subject of which is 'the origins, development, and expansion of capitalism as economic and social change'. Furthermore, their 'core proposition...is that class struggle has been central to the historical process'. In contrast, social history has been fiercely criticized for its lack of explicit theorization and a tendency to separate popular culture from the matrix of economic and political relationships in which it is embedded." (2)

Thus, we can see that Marxist historiography often places more emphasis on class conflict as a generator of historical change, which more general social history does not necessarily do.

As for examples? Edward P. Thompson's "The Making of the English Working Class" is generally regarded as a masterwork example of Marxist historical writing. I shall allow Matt Perry to explain its significance:

"The Making of the English Working Class was the most powerful expression of the gathering school of Marxist history, which took issue with the mechanistic traditions of official communist versions of history, looking ordinary people in the face as participants and makers of history...'history from below' or 'from the bottom up' became one of the most important contributions to the development of history since the Second World War. Harvey Kaye described The Making of the English Working Class as 'the most influential work of social history every written'. Thompson wove together his sources and narrative, and with each turn of the page, new witnesses testified: the middle-class observers, romantic poets, the moralising church leaders and the working-class radicals themselves. The book evoked an authentic feel for the period and rang with the voice of the exploited. Thompson set new empirical standards for Marxist history but successfully avoided what he considered the anathema of academic empiricism. May of his passages reflected his deep political passions and sympathies with the oppressed as well as a flowing literary style that revealed he had, like Marx, a love of poetry." (3)

I hope you found this useful! I would also recommend (though I didn't directly cite) Richard J. Evans' In Defense of History and Eileen Ka-May Cheng's Historiography: An Introductory Guide as good primers on historiography in general :)

Endnotes:

1: Georg G. Iggers, Historiography in the Twentieth Century: From Scientific Objectivity to the Postmodern Challenge (Wesleyan, 2nd edition, 2005), pp. 84-85.

2: Anna Green and Kathleen Troup, The Houses of History: A Critical Reader in Twentieth-century History and Theory (Manchester University Press, 1999), pp. 33-35.

3: Matt Perry, Marxism and History (Palgrave Macmillian, 2002), pp. 99-100