As with the element-wise conjugation action, for $H$ and $K$ subgroups of $G$ in the same $G\text{-orbit}$ under this action, say that $H$ and $K$ are conjugate.
I know that $Gs_o = \lbrace gs_o\ :\ g ∈ G\rbrace$ can be one orbit for G-orbits, but I am not just getting what "same $g\text{-orbit}$" means.
If I am somehow mistaken, can anyone show me where I got wrong in the meaning of G-orbits and relate it to the comprehension of the quote?