The key similarities are use of force and intimidation, taxation, hierarchy, and propaganda.
Once a criminal organization gets powerful enough, it becomes able to whitewash its own image and branch into legitimate/legal economic pursuits. Also, with sufficient growth and power, the very laws themselves can be bent to legitimize past and current actions.
Criminal organizations also utilize principles of decentralization as a scaling strategy. There are elaborate transfer of power rituals, some resembling democratic processes and others not.
The goal of any criminal organization is to become larger and more powerful, but there are extra spoils due to premium prices for black market endeavors. Criminal organizations seize opportunities where laws exist but are poorly enforced... or in other words, where there is no de facto prohibition against black/gray market activity (such as the tens of thousands of asian massage brothels in the US).
With additional revenue comes better propaganda and the freedom to clean up the organization's image. There is also a turning point when the group benefits more from harnessing moral indignation against certain behavior, and the wise populist criminal group will not let this go to waste.
China will make sure you go to school. China will make sure you have rice to eat. The mafia will make sure they get a piece of your rice and the school's lunch money. They're a selfish organization concerned with profit and not social issues, whereas the government's position is that the people matter.
If you want to compare government and organized crime, the Yakuza are probably the closest to a formal government. For example, they have some legitimate business interests and different tactics for gaining influence in multiple markets, they're more transparent than the mafia, and they're often altruistic.
However I'd argue that a stable, two-party corporatist government is essentially the same as a one party government.
Note that Hillary and Trump and Jeb are running pretty much the identical platform when you consider the substantive parts.
Governance in modern societies is implemented by a party which holds power over the state. The mafia have a business model which is similar, but largely limits itself to a few select types of business strategies and markets, much like many other businesses. Their use of a threat of force is unique in terms of business models, sure, but the mafia has nothing to do with governance in general.