I am studying stacks and I am experiencing some troubles understanding quotient stacks. If I have a scheme $X$ where a group scheme acts $G$ (let's suppose that everything is defined over an algebraically closed field of char $0$), I don't quite understand what is the relationship (if there is any) between the quotient stack $[X/G]$ and the quotient sheaf $X^{\bullet}/G^{\bullet}$ where the notation $\bullet$ means the functor of points. In particular, what happens when the action is free and transitive?
Thank you for your time, I am a noobie in this realm.