In this paper, we deal with orbital stability and Zhukovski\v{\i} quasi-stability of periodic or recurrent orbits in an impulsive dynamical system defined in the $n$-dimensional Euclidean space $\mathbb{R}^n$. In fact, we show that for a periodic orbit of an impulsive system its asymptotically orbital stability is equivalent to the asymptotically Zhukovski\v{\i} quasi-stability, and for a recurrent orbit the orbital stability is equivalent to the Zhukovski\v{\i} quasi-stability.