One of the most important challenges in diffeology is providing suitable analogous for submersions, immersions, and étale maps (i.e., local diffeomorphisms) consistent with the classical versions of these maps between manifolds. In this paper, we introduce diffeological submersions, immersions, and étale maps as an adaptation of these maps in diffeology by a nonlinear approach. We explore their behaviors from different aspects in a systematized manner with respect to plots, and especially, show that for manifolds, there is no difference between the classical versions and diffeological versions of these maps. Moreover, we introduce a class of diffeological spaces, called diffeological étale manifolds, and establish the rank theorem for them. It is also proved that a diffeological étale space on a diffeological orbifold is again a diffeological orbifold.