It seems to me like the building of castles has been a predominantly European affair. I know China and Japan built castles as well, but these seem to have been made out of wood, and on a smaller scale. To my knowledge, there aren't any surviving examples in China.
When did Europeans transition from castles to fortresses?
What did the Chinese do for fortifications and how do these compare to western fortresses?
It depends on what you're defining "castles" as.
The Forbidden City in Beijing or the Song palace in Hangzhou could qualify. In general, cities in China were also walled. Nanjing is a good example where you see a walled city (the longest extant city wall in China) with a fortress built in to the southern gate. Then you have the Ming Palace in the northeast.
If you can clarify what you mean as a castle then that might help in getting a clearer explanation.
Chinese fortifications tended to be more in the style of walled cities than the tall stone keeps we associate with "fairytale-style" European castles. Lots of Chinese cities had city walls with coincentric rings of fortifications, but two factors lie behind the fact that few of these structures remain today, and those that do have been heavily restored:
Many Chinese cities, including Beijing, traditionally had fairly extensive city walls. However, these massive walls of rammed-earth or masonry construction tended to get demolished during 20th-century urbanization. Compare the fate of the city wall of Medieval Paris -- they were extant right up until the 1840, when they were demolished because the walls were obstructing the urban growth of the city, especially the need to run modern roads and railways into the center of the city. The city wall of Beijing were demolished in the 1950s and 1960s under somewhat similar circimstances. To the best of the my knowledge, the city walls and "bell towers" of the Xi'an are the largest extant example of traditional Ming or Qing-era Chinese fortifications.
Many Chinese buildings were built most of wood with only the outermost walls and foundations being built of stone or earthworks. In this way, there are similarities to the "castles" of Japan. Consequently, unless these structures are constantly maintained for strategic or ideological reasons, they tend to burn down in time, if they aren't used for firewood or building materials first. For much of the 20th century, the Qing-era fortifications were seen as a sign of the hated former regime, rather than as valuable historical monuments, so they tended to not get preserved. In contrast, quite a few of the Buddhist and Confucian temples/shrines from the same era are in relatively good shape today -- they were viewed with greater importance to the daily lives of the local inhabitants than the government buildings were.
I had a bunch of good photos of all of these from when I visited China back in 2010, but that's hardly a reliable source, so if you'll give me until tomorrow morning I'll see if I can dig up some relevant sources (my undergrad East Asia books are in my parent's basement at the moment).
When did Europeans transition from castles to fortresses?
Around 1500 construction transitioned from the tall, relatively thin walls, of medieval castle building, to thick, low, sloping walls. The reason for this is simple, cannon. In 1494 Charles VIII invaded Italy, with a siege train of at least 40 cannon, which made short work of many of the exiting walls.
The walls that were built after that were better able to resits cannonfire. They also made better gun platforms than their predecessors. The star shaped configuration they were built in also allowed for overlapping fields of fire, which made approaching the walls extremely hazardous.