If it helps, I think of an astronaut as someone who sails among the stars, rather than to the stars. In that sense, it's just as accurate as cosmonaut. But, given that every living thing on Earth can rightfully be called an astronaut or cosmonaut, neither term is very precise. It is more precise to identify a person as human than to identify him as a cosmonaut, since cosmonaut can also refer to monkeys, rabbits, dogs, insects... :)
Cosmonaut, I believe, more literally translates to "spacenaut", which sounds terrible, because of the Russian word for space, which, like our cosmos, is derived from the word kosmos. The English term cosmonaut is not through the greek kosmos and nautis, but just an Anglicization of the Russian word.
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