There are several major differences:
1. Property is privately held in the US (though the US government does own substantial amounts of land, especially in the western US); in China, all land is nominally owned by the government, which issues "use contracts" (usually of 70 year duration) to companies and private citizens. This is a primary source of income for many municipalities (especially where land values are very high, such as in Shanghai) that lets them keep taxes relatively low.
2. While companies in the US are generally completely private or completely government-controlled (such as Amtrak or the Postal Service), many "State-Owned Enterprises" in China are controlled by the government yet openly traded on the stock market and have a great deal of private investment.
3. There are fewer labor regulations in China than in the US; minimum wages are generally much lower, and the "social welfare" system is still in it's infancy.
4. The Chinese economy is protected by tarriffs (which make importing high-end consumer goods such as electronics and cars very expensive) and a tightly controlled currency with exchange rates set by the central bank.