Allow me to do another explanation on the European country system, as I'm European. I won't need to tell you how these came to be. Like already said, multiple wars in the past have split up the land at various moments, in time this became Europe as we know it now. If you want to know more about the specific wars, ask Phoneix or Google/Wikipedia.
But the U.S. and Europe aren't actually that different, we just use different names.
The U.S. is the only country that uses the Dollar. Europe is the only nation that uses the Euro, with a few exceptions (British bastards, don't you agree Algernon?). So when it comes to the currency, we aren't that different.
The dividing of land and the way the law works are also not that different. For example, check out point 2 and 3 of this piece of copypasta. The language is a bit harsh, but it does the job.
But I'll continue either way. Each European country has its own law and taxes. But because of the European Union, we also share some laws and other stuff. Similar like each state in the U.S. has a different law, but yet you guys have a national goverment and everything. One result of the European Union is open boarders for the countries that are a member, likewise to you guys and the states.
Like the name U.S.A. already says, it are the UNITED STATES of America. In similar ways you can see Europe as the United Countries of Europe. We just call each section a country, you guys call it states.
We're not that different, the U.S. just had to feel fancy.