Of course this was an early Japanese legend and there was no record of Chinese words being used like Sessho (Regent) or Shosei, in the "Nihonshoki" it was called neither Sessho nor Shosei.
むろん伝説時代のことであるので当時に摂政だの称制だのという漢文の用語が使われたわけもなく、古事記では摂政とも称制ともいってはいない。