The words amateur and professional are antonyms.
Most amateur Go players play the game for fun, as a hobby. However, there are many tournaments that are catered for amateurs, with the World Amateur Go Championship as one of the high profile ones.
In the world of go, there has normally been a quite clear distinction between amateur and pro tournaments. Things have changed a little, quite recently.
The Japanese tradition was that insei do not play in amateur tournaments; certainly not as part of their training. Amongst insei who do not become professional you can find some of the strongest 'amateur' players; so in this case a top amateur might be a student pro, who decided to go to university instead of becoming an actual pro. It used to be unusual for future pros to come from amateur go circles (Kageyama was an exception).
On the other hand, in China, it used to be normal for the strongest amateurs to compete in the WAGC, before turning pro. In that way players such as Ma Xiaochun played as amateurs, on their way to becoming title holders. In China national tournaments for amateurs can give a chance to the winner to play as pro 1 dan, for some short period (as a candidate pro).
In South Korea promotion to pro is now regulated by a very tough league (with 80 players), only four becoming pro each year. The old system, described in First Kyu, changed many years ago; it gave a chance to 1 gup players to become pro. In South Korea there is now a genuinely Open tournament, in which any player in the world can (in principle) qualify.
The Fujitsu? international pro-am tournament allowed a few top amateurs to qualify from around the world, getting games against pros. This has become more interesting, since upset victories are now not so rare.