When the government owns companies

So the U.S. government bailed out the insurance giant AIG. But we did not just bail it out by giving it a loan or guaranteeing its solvency. We bought 80% of its equity. So the U.S. government now essentially owns it. The government also “seized” ownership of Fannie Mae, which I admit was a strange sort of public/private hybrid. But when the state owns companies, isn’t that socialism? (Someone please correct me if I’m interpreting all of this incorrectly.)