I read from this answer and understand that the homogenous coordinates is of the form $[x, y, z]$ which represents by square bracket. Also read from this answer the homogenous coordinates is of the form $(x, y, z)$ which represents by first bracket.
My question is what is the right representations of homogenous coordinates or how both representations are right at the same time?
Different people may write projective coordinates as $(x,y,z)$, $(x:y:z)$, $[x,y,z]$, or even $[x:y:z]$. All have the same meaning, as long as the context makes it clear that those are indeed projective coordinates (the first option may be confused by affine coordinates, but the space where those coordinates live is usually clear from the context).
I understand that you wished another answer, but it just doesn't exist. There's no "best" notation or "universally accepted" notation. As long as everyone understands what is being said, which is very often the case, all is fine.