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Answer:
Clarisse is a demigod, daughter of ares, who prefers to bully via violence over insults. Where as Nancy Bobofit is a mortal, who prefers to bully via insults. Both are rude to Percy with somewhat petty reasons for doing so. Clarisse's being that Percy gained some respect from killing the minotaur, and drenching her in toilet water; and Nancy Bobofit's being that she is a Kleptomaniac. (in the musical her reason is because Percy told her to stop wedgie-ing the first graders)
I hope that made sense, sorry if it didn't
have a nice day! :)