Terminology for a certain image of an action

Question

Let $R$ be a commutative ring. Let $M$ be a left $R$-module. Then for every $\lambda\in R$ the set $\lambda M$ is a submodule of $M$. Does this submodule have name? What is the analogous object in the realm of group actions called (i.e. given a set $X$, a group action $\alpha \colon G\times X \rightarrow X$ and a group element $g\in G$, what is the image of $\alpha(g,–)$ called)?