What is the difference between the PLO and the PA as Palestinian governing bodies ?

The PA is only supposed to represent Palestinians in the occupied territories. The PLO is supposed to represent Palestinians everywhere, a majority of whom live in exile outside of Palestine/Israel, prevented from returning by Israel because they aren’t Jewish. The PLO is also legally responsible for conducting negotiations with Israel.
Since it was established, the PA has been dominated by the Fatah party, first led by Yasser Arafat and then current PA President Mahmoud Abbas. Since the 1960s, Fatah has also dominated the PLO, which is supposed to be an umbrella organization representing all Palestinians.