"...since you asked about the difference between private corporations and a government allegedly of the people, by the people, and for the people. By the rules of the free market, corporations and people are in a permanent state of war, and caveat emptor. By the rules of the Constitution, the government is supposed to be accountable to us."

The people "vote" everyday on the market- you decide whether you eat at Burger King or Mcdonalds [or not].
And by the rules of America Constitution, the govt is thwarted from doing too much. One of the main concern of the Framers was prevent government for controlling to much- they looked Europe and knew the lack of freedom that the system created, thereby created a govt system that checked govermental power.
Corporations are not a essential aspect of free enterpise, they mostly a response to government. Tax laws basically require corporations whereas partnerships and business associations would be more common without these laws.

"Early corporations of the commercial sort were formed under frameworks set up by governments of states to undertake tasks which appeared too risky or too expensive for individuals or governments to embark upon. The alleged oldest commercial corporation in the world, the Stora Kopparberg mining community in Falun, Sweden, obtained a charter from King Magnus Eriksson in 1347. Many European nations chartered corporations to lead colonial ventures, such as the Dutch East India Company, and these corporations came to play a large part in the history of corporate colonialism.

In the United States, government chartering began to fall out of vogue in the mid-1800s. Corporate law at the time was focused on protection of the public interest, and not on the interests of corporate shareholders. Corporate charters were closely regulated by the states. Forming a corporation usually required an act of legislature. Investors generally had to be given an equal say in corporate governance, and corporations were required to comply with the purposes expressed in their charters. Many private firms in the 19th century avoided the corporate model for these reasons (Andrew Carnegie formed his steel operation as a limited partnership, and John D. Rockefeller set up Standard Oil as a trust). Eventually, state governments began to realise the greater corporate registration revenues available by providing more permissive corporate laws. New Jersey was the first state to adopt an "enabling" corporate law, with the goal of attracting more business to the state. Delaware followed, and soon became known as the most corporation-friendly state in the country after New Jersey raised taxes on the corporations, driving them out. New Jersey reduced these taxes after this mistake was realised, but by then it was too late; even today, most major public corporations are set up under Delaware law."
http://en.wikipedia.org/wiki/Corporation

Corporation and monopolies are the children of govt or could be said to depend on their existance solely due to governmental law. It's foolish to assume it's corporations vs govt- what is the true bane of corporation or monopoly is free enterprise with free markets and economic competition [free meaning lack of governmental rule prohibting trade/exchange of goods- or perhaps better explained as, simple/miminal laws so as not to require an army of lawyers to win the day].