"Level" makes sense when regarding a stage, if you think of it in terms of floors. First floor, second floor, etc. can be referred to as levels of a building. "Map" makes sense too, because the stages literally are maps and you get actual maps of the areas too (in some cases). Was about to say stage wouldn't make sense, until I thought about how it could be applied to plays, where they act everything out on a stage. Games wouldn't be too different from this.
However, I'm not sure about "level" in terms of character strength. Perhaps going by the phrase, "They're on a whole other level" it might make sense? In which case, it's almost more like leagues. Leagues ahead of others. Could also go back to the floor idea, where you literally go up levels, but I wouldn't be too sure on that one.
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Many a false step is made by standing still