>>>The Vilna Gaon is who people refer to when saying “The Gaon”. The Rogotchover I don’t believe is ever referred to by that title, he’s always “The Rogotchover Rebbe”.
In Chabad also “the Gaon” refers to the Vilna Gaon, though he is usually referred to as Vilna Gaon or Gra.
I’ve never heard anyone refer to the Rogatchover as “the Gaon” but neither is he called “rebbe”.
I think he is universally called “the Rogatchover gaon” or הגאון הרוגצ’ובי