During rebonding of hair, reaction conditions is heat under reflux (that giant upside-down fishbowl) with reducing agent, to reduce (ie. add hydrogen) and hence break the -CH2-S-S-CH2- disulphide bridges of the hair keratin protein molecules, that makes hair curly. So you get straight hair.
During perm(anent) curly hair process, after curlers are in place at desired locations, reaction conditions is heat under reflux (yeah, that fishbowl again) with oxidizing agent, to oxidize (ie. remove hydrogen) and hence create the CH2-S-S-CH2- disulphide bridges of the hair keratin protein molecules, that makes hair curly. So you get curly hair.
Therefore, the term "REBONDING" refers to first destroying the disulphide bonds that hold hair in its current curly configuration, then after straightining it, RE-making the disulphide BONDS that hold the hair in its current straight configuration.