In the US, there is no difference in the manner in which a company is originally set up. Once a company is incorporated, then it may endeavor to go public, but generally only after some time in business so as to establish a track record.

Under Federal law, you can offer just about any sort of security in almost any sort of company, you just need to disclose all and cut through tons of red tape. And you'd best have experienced CPA's on board - very important in getting registered to publicly offer securities.  

Many states have stricter standards than the Federal law (Securities Act of 1933 and billions of regulations promulgated thereunder), so beyond having to disclose all, many state regulators need to decide if the offering is fair.  Some states are more paternal than others. State securities laws are know as "Blue Sky" laws.  

But I don't know a thing about going public in China. Not likely to be vastly different though.