Chromium is the open-source version of the Chrome browser (both from Google) and is mainly found on Linux platforms. It is missing a few features like Flash and some video codecs.
Windows and Mac users can run Chromium but unless you are really passionate about open-source I would stick to Chrome.
Other browsers out there include: Firefox, Maxthon, Yandex and Opera. Personally, I now use Maxthon or Yandex, as Firefox was starting to annoy me because it kept forgetting form entries and passwords and the popup boxes were getting in the way all the time.
BTW, there is no browser called “Google” — Google is a search engine that can be reached on any browser. And of course, don’t forget…friends do not let friends use Internet Explorer!…unless you are some kind of sado-masochistic monk on a 56k dial-up modem.