How were pirates from Eastern countries, like China, different from the Western pirates? In regards to their customs, culture, way of doing things, etc.

I've only really read about Chinese pirates, so I can't really comment on Western pirates. However, hopefully an overview of Chinese piracy might answer your question. My source for this post is the monograph Like Froth Floating on the Sea: The World of Pirates and Seafarers in Late Imperial South China. I no longer have a copy of the book, so I'll keep the facts related to information from the book I have in my own notes from the book, and information that I was able to verify without a copy in my hand.

Piracy in the late eighteenth and early nineteenth (1780-1810) centuries was mostly practised by poor fishermen who were trying to supplement their income in the off season or to pay off their debts. This was because the return on being pirate would often outweigh the return on being a legitimate sailor. For example, a sailor would either be paid in food, cargo space, or cargo. But this share would be so small that the pirate would spend most of their life in debt, often to the fishmonger or merchant that they sold their goods to, to the point that this debt would be necessary to just to buy enough food to eat. In other cases, a fisherman who would work on a boat would turn to piracy to gain enough income to order to buy a boat to start his own fishing operation. At the time, the choice to become a pirate would have seemed logical to sailors since there was little chance of upward mobility. Aside from spending so much time on the seas, moving from port to port in search of work, very few families would give up their daughter in marriage to a sailor because they were socially so low. Pirate ships were also frequently crewed by the unwilling. These people were forced to serve on pirate ships as captives. They would perform menial tasks for the freer crew. Often they would outnumber the actual free pirate crew.

Piracy occurred outside the social norms of the time period (Confucianism doesn't exactly leave much room for extolling the virtues of piracy), and they reflected this. They would sometimes worship their own gods, were known to be given to vices such as gambling and binge drinking. Beyond the common whoring, it would not be uncommon, and in cases would be considered a rite of passage, for a young, new member of the pirate crew to have a homosexual relationship with a senior member of the crew.

This space also left room for women to lead a very different life than would have been available to them at the time. Some women willingly chose to live as pirates. They would be able to have their own income and independence. One difference from Western pirates (according to Antony) was that women would be able to serve openly as women, without disguising their gender. They could rise up through the ranks very high. For example, Zheng Yi Sao commanded an entire pirate fleet and her husband's death (wiki says around 300 ships and 20-40,000 crew, but I can't confirm that myself).

During this time period, the pirates grew to be fairly powerful on the Southern coast. Their gained economic power by selling back stolen goods at a discount, helping business sell at a better rate or at a higher leel of profitability. This quote from the author in an article puts it better than I ever could:

At the height of their power huge pirate leagues gained firm holds over many coastal villages and port towns, as well as over shipping and fishing enterprises, through the systematic use of terror, bribery, and extortion. During such times all ships operating along China’s coast were liable to pirate attack unless they bought safe-conduct passes. To avoid attack, merchant and fishing junks paid protection fees to the pirates, who in turn issued passports guaranteeing impunity to the purchaser. In the early nineteenth century pirates had virtual control over the state-monopolized salt trade, and even Western merchants had to pay ‘tribute’ to the pirates to protect their ships. The extortion system was highly institutionalised with registration certificates, account books, full-time bookkeepers, and collection bureaus. Extortion was not only a major form of pirate income, but the basis of their regional domination. Pirates were able to penetrate the structure of local society through the establishment of protection rackets. Extortion was the most direct and effective way that pirates exercised hegemony over an area. Pirates actually constituted a level of control over maritime society that operated independently of and even overshadowed that of the government and local elites. Piracy therefore became a significant and pervasive force in South China’s coastal society.

So you can see that they grew very powerful indeed, with their own internal passport system, and even the need for a kind of bureaucracy to maintain their power. I do recall that they could and did operate with brutality. I recall in particular one case of nailing the feet of an enemy to the deck of the ship. However, this was also during a time when the state also practiced their own brutal measures, such as Death by 1000 Cuts (I do not recommend Google image searching this). Unfortunately, I don't have any more specific examples on hand that I can reference, so I'll leave it at that.

Anyways, I hope this helps answer your question! The article I referenced above is short, easy to read, and might provide more information if you're curious. I wanted to finish this post with a quote about the flavour of Chinese pirate grog, but unfortunately I don't have the book on hand and would prefer to give you the quote in its full glory. I'll end it in if I go by the library this week. Let me know if you have any follow-up questions, and I'll do my best to answer!