  Recently, twistor-like formulations of tree amplitudes involving $n$ massless
particles have been proposed for various 6D supersymmetric theories. The
formulas are based on two different forms of the scattering equations: one
based on rational maps and the other based on polarized scattering equations.
We show that both formulations can be interpreted in terms of a symplectic (or
complex Lagrangian) Grassmannian, $\mathbb{LG}(n, 2n)$, and that they
correspond to different ways of fixing the ${\rm GL}(n, \mathbb{C})$ symmetry
of $\mathbb{LG}(n, 2n)$. This provides an understanding of the equivalence of
these different-looking formulas, and it leads to new twistor-like formulas for
6D superamplitudes.
