The nouns “onset” and “outset” mean the same thing, which is “beginning,” “start,” or “commencement,” but their usage and syntax differ so they can’t be used interchangeably. We say “Inspection of the city's drainage canals were done at the onset of the rainy season” but not “Inspection of the city's drainage canals were done at the outset of the rainy season.” On the other hand, we say “We told you at the outset that she will surely lose” but not “We told you at the onset that she will surely lose.”