Budweis is the German name for Budevice. Most Czech towns have a Germanic form of the name. It's the same place. And there is no more Czechoslovakia. They split up in 91 during the velvet divorce. So there is the Czech Republic and Slovakia.
In Czech, the name of Budweis is Budejovice. Czechvar is the trade name of Budweiser Budvar in the US. It is
the same light-colored pilsner-style lager as Budweiser Budvar. Adolphus Busch took the name from that brewery because he liked the name--AB Budweiser beer has never been related, other than it is a light lager. He trademarked the name first, so Budvar has to use the Czechvar name in the US. This due to a 1939 agreement in which the Czech brewery relinquished any use of the brand name in North America.
Saying that "The Americans got hold of it and made it into watered down piss" isn't exactly correct. The name only was taken by a German and brought to the US to be put on a new product, albeit an attempt at "emulating" a Czech pilsner--and admittedly a poor one at that.
Oddly enough, Anheuser-Busch has the sole US distribution contract with Budweiser Budvar for Czechvar (and Stella Artois, BTW). More on that here:
http://www.cbsnews.com/stories/2007/01/08/business/main2337011.shtmlI have a full can of Budweiser Budvar on my bar downstairs, and I've enjoyed a Pilsner in Prague too, but it doesn't necessarily mean I know anything.