What time frame are we talking here? For the early Qing (1644 to around 1800) the overwhelming majority of Chinese migration was within the polity of the Qing Dynasty. See Peter Purdue's Exhausting the Earth on demographic influx into Hunan. Dai Yingcong also talks a lot about migration into Sichuan from the coast, in The Sichuan Frontier and Tibet: Imperial Strategy in the Early Qing. Wang Di estimates that a total net of roughly 8.5 million people migrated from the east to Sichuan between 1680 and 1820. To give you an idea of the scale of this migration, that would be roughly six times the number of Europeans that moved from Europe to the New World from Columbus all the way to 1800.

We see a similar story in other hinterland provinces like Manchuria, Yunnan, and Guizhou, where the Han population increased from about 1.5 mln to 12 mln people.

Now, after 1820 we do see outward migration from China. From 1820 to 1949 about 20 mln people migrated from China to SE Asia, where many of them maintain vibrant communities to this day. This is also when we begin to see "China towns" cropping up in the west.