The ELI5 for China is pretty much the same as for any other huge country: conquest and colonization. The original center of what we usually consider Chinese civilization is the lower Yellow River region and the Wei river valley. From this base the population spread south and southwest gradually. The southwest Sichuan basin was brought into the fold through Qin conquest. The south experienced gradual migration that really took off with the spread of high yield rice agriculture. During the Han-Sui interregnum the south from the Yangtze to the Pearl River Delta became core regions of China as well, and the Yangtze was linked to the Yellow River with the Grand Canal. The far southwest (Yunnan, Guangxi, etc.) was incorporated into the empire through large scale migration helped by a copper mining boom in the 18th century. The far northeast was incorporated through the Manchu conquest followed by large scale migration in the late 18th through 19th centuries. The far west was incorporated through military conquest and government sponsored colonization starting in the 18th century. Taiwan was incorporated initially by Ming rebel regimes then occupied by the Qing government, which again led eventually to large scale colonization.

Russia just happened to be close to Siberia and northeastern Europe. These were vast tracts of land that, because of climate, relative isolation and distance, had a low population density and were not claimed by any major power at the time. So the Russians just ... moved in. The process was actually more complex than that and there are plenty of posts in this subreddit that will provide more detail. Essentially, though, it was fairly similar to how many Europeans colonized the New World .. except that the Russians didn't have to cross an ocean to do it. Also unlike colonies, these new lands became integral parts of Russia. The primary motivation seems to have been commercial interests such as pelt trade and collecting tribute from native tribes.

tl;dr Viking slave traders were conquered by the Mongols then conquered most of the Eurasian Steppe. Kinda.

Russian history is complicated, but I'll hit the relevant highlights. Moscow was founded by viking slave traders who were selling the locals down the river the the Byzantines. Most of "European Russia" was European-ized (kinda) by these viking types. After a couple of generations the vikings went native and became local lords known as the Varangian Rus; e.i. Russians

Fast forward a couple of centuries.

The Russians were eventually conquered by the Mongols. After Genghis Khan died, the Mongol Empire was distributed to his decedents who ruled the empire in chunks. The Golden Horde controlled most of the Ukraine, Western Russia, Georgia, the Urals, the Northern Caucasus's, and a huge chunk of Siberia.

After the Mongols were expelled, the new Russian government retained much of its land mass. The rest they fought to retake over the centuries. By the height of the Russian Empire, they controlled most of the land between the Eastern European States and the Pacific Ocean.