How do you differentiate the English definitions from what the Torah differentiates between a 12 and 13 year old?
The rights and responsibilities which the secular world conveys upon one who reaches the age they consider to be an adult (generally, 18) are vastly different than the dinim which apply to a bar or bas mitzvah.
For example, the right to vote or buy cigarettes and alcohol don’t have a parallel in halachah, and the ability to be motzi someone in Kiddush or Birchas Hamazon doesn’t exist in secular law l’havdil.