  Using the orbit method we attempt to reveal geometric and algebraic meaning
of separation of variables for the integrable systems on coadjoint orbits in an
$\mathfrak{sl}(3)$ loop algebra. We consider two types of generic orbits
embedded into a common manifold, endowed with two nonsingular Lie-Poisson
brackets. We prove that separation of variables on orbits of both types is
realized by the same variables of separation. We also construct the integrable
systems on these orbits: a coupled 3-component nonlinear Schr\"{o}dinger
equation and an isotropic SU(3) Landau-Lifshitz equation.
