How is the Mexican government different from the US government?

The Mexican system of government is very similar to its American counterpart. For one thing, it's a federal system with a clear separation of powers between the executive, legislative, and judicial branches. Nevertheless, there are a number of differences between the two systems. For example, representatives of the lower house of the Mexican Congress, the Chamber of Deputies, serve three-year terms, whereas their American equivalents in the House of Representatives serve only two.
The biggest difference between the two systems comes in relation to presidential elections. In the United States, the President is limited to no more than two four-year terms. In Mexico, presidential elections are held every six years. Once elected, the President is restricted to serving just one term. And once he leaves office, even if he only served for a short time in a caretaker capacity, he can never be President again. This principle emerged from the Mexican Revolution of 1910–1920, which came about largely as the result of widespread anger at President Porfirio Diaz's continual reelections—often in dubious circumstances—for over 25 years.
Unlike the United States, Mexico has a multiparty system, though three parties tend to dominate political life. As such, alliances and coalitions are a normal feature of Mexican politics in a way that simply wouldn't be possible in the United States. In Mexico, political parties must secure 2% of the vote in federal elections if they are to be formally registered by the INE, the institution in charge of organizing those elections. Meeting this threshold of support entitles political parties to public funding, something else that sets the Mexican system apart from that prevailing north of the border.