Module and group ring: definitions and notations

Question

I apologize in advance for the stupid questions and the bad English, but I've started studying math a few months ago. I've some problems with the definitions of a group ring, modules, and their notations. I've found in a textbook, the expression "$R[G]$-module" (Robinson textbook) (where $G$ denotes a group and $R$ a ring). How should I read it? I mean: I know that the expression $A$-module indicates a module over a ring $A$ and the expression $R[G]$ indicates the group ring of $G$ over $R$; so when I find "$R[G]$-module" should I take $A=R[G]$ (because if $R$ is a ring then $R$ is always an $R$-module on itself, right?)? Moreover, I read that a group ring $R[G]$ is a free module and at the same time a ring, constructed from any given ring $R$ and any given group $G$. Is there a relationship between $R[G]$ (considered as a free module) and an $R$-module consisting of an abelian group $(G,+)$ and an operation $R×G\rightarrow G$? Thanks in advance to everyone!