I. Histories:

    Simplest: chronicle, like the Anglo-Saxon Chronicles, which which my favorite entry is:

A.D. 1026.  This year went Bishop Elfric to Rome, and received
the pall of Pope John on the second day before the ides of
November.

A.D. 1028.  This year went King Knute from England to Norway with
fifty ships manned with English thanes, and drove King Olave from
the land, which he entirely secured to himself.

Apparently nothing noteworthy happened in 1029.  At base a chronicle is an enumeration of who did what to whom, when.  Schemes of "event data" commonly used in the social sciences are of this type.  The identity of a actors is only implicit; there is no information provided about their motivations, and nothing of the "internal" states of actors (e.g., about their information processing) is offered.  Thus the kinds of inferences that we can draw from chronicles is limited. [Hedley Bull's criticism of behaviorism.]

    Complex: story, like the Russian fairy stories studied in the 1920s by Vladimir Propp.  He found limited varieties of plot structures utilizing some 50 transformation, offered in a strict linear order.  The same sort of analysis, presupposing strong, invariant structures, have been applied to other literary forms, perhaps with most success to religious texts.  (The Wikipedia article on structuralism appears to me to be quite useful.)

A story often introduces some figure as protagonist who pushes events along.  It also usually general attributes to idividuals and groups such  attributes such as good/evil, strength/weakness, activity/passivity ('dimensions' of the semantic differential), and others.  It may claim moral significance to itself in whole or part (as fable, myth, moralistic story).

   Other literary forms include account, annals, autobiography, biography, diary, epic, journal, memoirs, narration, narrative, prehistory, recapitulation, recital, record, relation, report, saga, tale, version

   "Academic" histories may seek to narrate events or to demonstrate causal connections among events or to validate a full-fledged theory (here treated as a logically connected set of knowledge claims).

Regional histories:

Lampe's history jumps from episode in one country to comparable or contrastive episode in another.  He does not tell us how he demarcates the episodes.  He does tell us -- and more crucially is quite consistent in his practice -- how he determines episodes to be comparable.  In particular, his basic dichotomy is to compare the experiences of countries which had to accommodate huge numbers of ethnically similar refugees, and separately to compare the experiences of countries which tried to assimilate large ethnic minorities.

More generally, two approaches are often taken:

Cross-national comparisons: presupposes same dynamic, e.g, of "development" 

Longitudinal comparisons: pertains to one "society"

A regional history must combine both. 

Under certain restrictive conditions, such things as pooled-time series : for  example, N people measured for a number of variables in T successive periods.   However, unless we believe that roughly the same dynamic applies to all observed subjects, we can't say enough about the unmodeled disturbances to create an adequate estimator.  Where the N "people" are instead closely interacting "countries," there is no clean way to pool or integrate time series.

II. How have social scientists typically addressed the historical study of  a "region"?

Skocpol-Somers identified three approaches to historically-sensitive comparative inquiry, which they name macro-causal analysis, parallel demonstration of theory, and contrast of contexts.  What are advantages and disadvantages of each?

By the way, Walter Scheidel offers a succinct statement of these and other approaches in a quite different historical setting.  See also  Criag Calhoun's critique of Skocpol-Somers' proposal as part of a larger assessment of 'historical sociology'.

...

This trichotomy, though heuristically useful, is somewhat out of date: see Kevin D. Hoover, Causality in Macroeconomics (Cambridge University Press, 2001), and the many reviews thereof.

III.  Suppose we find that that causal [historical] processes within "a region" differ markedly.  Then what do we infer?