Astronaut is an English term for a person who professionally operates a craft or carries out a mission outside the Earth's atmosphere. The word is constructed from the Greek ástron, meaning star, and naútēs which means sailor. So, technically, an astronaut is a 'star sailor.' NASA and the U.S. Government in general recognize thoses who travel above 50 miles of altitude as astronauts. Thus, not only those who fly dedicated spacecraft qualify - the pilots of the U.S. X-15 program, which reached altitudes over 50 miles, have all been officially designated astronauts although the civilian members weren't so recognized until 2005.
Astronauts may be military, civilian, or commercial. Generally, military and civilian astronauts are members of a government spaceflight program and differ depending on whether they are active members of the military, and commercial astronauts are part of a non-government corporate one. The first commercial astronaut was Mike Melvill, who piloted SpaceShipOne above the 50-mile demarcation as a test pilot for Scaled Composites.
It should be noted that NASA and the Russian Federal Space Agency have agreed to call paying tourists who travel into space 'Spaceflight Participants' to distinguish them from astronauts.
The terms cosmonaut and taikonaut are Anglicized constructions indicating astronauts of a particular political affiliation - Soviet/Russian in the case of cosmonaut, and Chinese in the case of taikonaut. Although cosmonaut is an Anglicized version of the official Soviet and Russian term (космона́вт, or "kosmonavt"), taikonaut was originated on an internet newsgroup. The Chinese government refers to its astronauts as 'astronauts' in English-language press releases, and 'космона́вт' in Russian.