This is from Wikipedia, so all I can do is hope the source is reliable:

By convention, a space traveller employed by the Russian Aviation and Space Agency or its Soviet predecessor is called a cosmonaut. "Cosmonaut" is an anglicization of the Russian word космонавт (kosmonavt), which in turn derives from the Greek words kosmos, meaning "universe" and nautes, meaning "sailor".

In the USA, a space traveller is called an astronaut. The term derives of the Greek words ástron ("star") and nautes, ("sailor"). For the most part, "cosmonaut" and "astronaut" are synonyms in all languages, and the usage of choice is often dictated by political reasons. However in the United States, the term "astronaut" is typically applied to the individual as soon as training begins, while in Russia, an individual is not labelled a cosmonaut until successful space flight. On March 14, 1995 astronaut Norman Thagard became the first American to ride to space on-board a Russian launch vehicle, arguably becoming the first American cosmonaut in the process.

European (outside of the UK) space travellers are called spationauts (a hybrid word formed from the Latin spatium, "space", and Greek nautes, "sailor"). While Europe has not yet produced manned spaceships, it has sent men and women into space in cooperation with the Soviet Union, and, to a lesser extent, the United States of America.

Taikonaut is sometimes used in English for astronauts from China by Western news media. The term was coined in May 1998 by Chiew Lee Yih from Malaysia, who used it first in newsgroups. Almost simultaneously, Chen Lan coined it for use in the Western media based on the term tŕikōng (太空), Chinese for space. In Chinese itself, however, a single term yǔháng yuán (宇航員, "universe navigator") has long been used for astronauts and cosmonauts. The closest term using taikong is a colloquialism tŕikōng rén (太空人, "space human") which refers to people who has actually been in space. Official English text issued by the Chinese government uses astronaut.

Hmm--the Cyrillic and Chinese characters copied straight into my text window, but a preview indicates that they're going to post as gibberish. Sigh.