  By considering the superembedding equation for the Type II superstring we derive the classical relation between the NSR string and the Type II GS superstring Grassmannian variables. The connection between the actions of these two models is also established. Then introducing the proper twistor-like Lorentz harmonic variables we fix $\kappa-$symmetry of the GS formulation in the manifestly SO(1,9) Lorentz covariant manner and establish the relation between the gauge-fixed variables of the NSR and the Type II GS models. 
On covariant $\kappa-$symmetry fixing and the relation betwen the NSR   string and the Type II GS superstring