Budweiser is a Czech beer that has been brewed since the early 17th Century. The Americans stole the name, and would have grabbed the beer too were it not for Vaclav Havel. American budweiser has to be sold on the continent as bud, although, shamefully not in the UK, the name budweiser is reserved for the Czech brew.
They are two separate beers, they share a name, but nothing else. Czech beer is the best beer in the world btw.
My mouse is playing up, otherwise I would post a link, google budweiser budvar. In America the beer is called Czechvar.