I'm interested in how historians tend to describe different post-Qin Chinese dynasties as different succeeding states (e.g. Ming Empire, Empire of the Great Qing, etc.). In contrast, European ruling families seem to be treated as succeeding regimes of the same state (e.g. York, Tudor, Stuart, but always the Kingdom of England).
Is this just a difference of each nation's historiography? Should I view Imperial China as one state with many ruling families, or as a historical period describing multiple states?
If you're talking specifically post-Qin, there are huge variations in levels of continuity (or noncontinuity) between subsequent dynasties. I'm not knowledgeable enough first-hand to comment in detail on the subject, but I'm reading Wolfram Eberhard's A History of China, which is available for free on Kindle. Certainly around the Three Kingdoms (right after Han) and then around the Northern and Southern Kingdoms (right after Jin, before Sui) the country had fragmented into largely separate landed polities vying for control. The Three Kingdoms fragmentation lasted six decades; the North-South Kingdoms lasted over a century and a half. These are significant enough that I would consider "Qina" as a state to have broken up during those times, and thus the concept of unbroken imperial rule from Qinshihuang to be untenable.
In addition, there was the constant external pressure by various non-landed ethnic groups, which themselves did not exist in a state of unchanging stasis, but also intermarried, supported, betrayed, opposed, and otherwise interacted with the people of the post-Qin kingdoms. Eberhard's recounts a dizzying array of peripheral clans, muting from one to the next, sometimes seizing power and marrying into the settled families and kingdoms. Xiongnu, Huns, Turkics, Sogdians, Uyghurs, and Tibetans are all mentioned as key concerns with profound effects on the stability of the central cosmopolitan regions.
While Qinshihuang was the first ruler to declare himself an emperor with the title of Huangdi, Eberhard maintains (and I agree) that it's oversimplistic to claim that he "founded China as we know it". Later non-Imperial kingdoms exceeded his territory, influence, and population individually without ever unifying the nation.
Instead, Eberhard terms "modern China" as starting from the late Sui and early Tang, whereupon a historian could more confidently claim an unbroken (or near-unbroken) line of Imperial command across dynasties. Prior to that, when empires collapsed into long-term squabbling intermediary kingdoms, Eberhard terms the period of "medieval China".