The word "Astronaut" comes from the Greek for "Star Sailor" and was coined by author Neil Jones in 1930. It is used for space-faring people in the U.S. or on American missions.
The word "Cosmonaut" is used to refer to Russian astronauts and comes from the Greek for "Universe (Cosmos) Sailor"
While the Chinese government uses the words "astronaut" and "cosmonaut" many English-language media use the word "Taikonaut", from the Chinese word for "Space" ("taikong") along with the Greek for "Sailor" ("naut").
It seems the rule is that any nation that sends people into space needs their own word for what to call its space-pilots. Now that India is in the game (first flight scheduled for 2015), they need a word as well.
The Sanskrit for "Space" (or "Sky") is "Vyoma" and so their word is "Vyomanaut" (vee-OHM-uh-naut) according to the Indian Space Research Organisation.