Introducing someone as a ‘friend’ communicates more commitment to the Hungarian than what you probably mean using this word, especially if you come from the American culture. It takes time for someone to call you his friend in Hungary, and if it happens, you are one of the few chosen ones. Americans tend to have a low wall on the outside, and a higher one on the inside. Hungarians have a higher wall on the outside, but once you are in, you are in.
For more, spend some time perusing this indispensible guide to the Inner Hungarian. :)