America's Capitalism

I don't understand capitalism very well. But I can't wrap my mind around how government bailing out corporations is part of free enterprise. I thought capitalism had to do with government hands-off. If the government is dumping billions of dollars into private companies, do they then become government entities? Or do they become owned by the American people because the taxpayers are giving them their money? Is it constitutional for the government to favor big businesses? Why can't small businesses get bailed out too? If the corporations are rewarded with get-out-of-jail-free cards, I think it only fair that small business owners should too. Am I getting this confused with laissez-faire? Please explain this too me!