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We prove a uniform version of the Dynamical Mordell–Lang Conjecture for étale maps; also, we obtain a gap result for the growth rate of heights of points in an orbit along an arbitrary endomorphism of a quasiprojective variety defined over a number field. More precisely, for our 1st result, we assume |$X$| is a quasi-projective variety defined over a field |$K$| of characteristic |$0$|⁠ , endowed with the action of an étale endomorphism |$\Phi $|⁠ , and |$f\colon X\longrightarrow Y$| is a morphism with |$Y$| a quasi-projective variety defined over |$K$|⁠. Then for any |$x\in X(K)$|⁠ , if for each |$y\in Y(K)$|⁠ , the set |$S_{x,y}:=\{n\in{\mathbb{N}}\colon f(\Phi ^n(x))=y\}$| is finite, then there exists a positive integer |$N_x$| such that |$\sharp S_{x,y}\le N_x$| for each |$y\in Y(K)$|⁠. For our 2nd result, we let |$K$| be a number field, |$f:X\dashrightarrow{\mathbb{P}}^1$| is a rational map, and |$\Phi $| is an arbitrary endomorphism of |$X$|⁠. If |${\mathcal{O}}_{\Phi }(x)$| denotes the forward orbit of |$x$| under the action of |$\Phi $|⁠ , then either |$f({\mathcal{O}}_{\Phi }(x))$| is finite, or |$\limsup _{n\to \infty } h(f(\Phi ^n(x)))/\log (n)>0$|⁠ , where |$h(\cdot)$| represents the usual logarithmic Weil height for algebraic points. [ABSTRACT FROM AUTHOR]