I thought that it was the same scramble from the top, everyone posting a single move in order to reach a solved puzzle. Am I wrong about that?
You are right. Once the puzzle is solved, another scramble might be posted to continue the game for future players.
Players can choose whichever move they will make - e.g. they can start with F2L but then they can switch to Roux. There is no preferred method during the whole solution. If you see a good move, post it and hope the next solver will follow your solving approach .