Do "$R_*$-modules" have an accepted name?

Question

(All my rings are commutative and unital.)

By a module, I mean an ordered pair $(R,M),$ where $R$ is a ring and $M$ is an $R$-module. There is a functor $$\mathbf{ur} :\mathbf{Ring} \leftarrow \mathbf{Mod}$$ that returns $R$ given $(R,M),$ namely the underlying ring functor.

Now let $X$ denote a topological space and $R_*$ denote a sheaf of rings on $X$. Then by an $R_*$-module, I mean a sheaf $M_*$ of modules on $X$ satisfying: $$R_* = \mathbf{ur} \circ M_*$$

Question. Do "$R_*$-modules" have an accepted name?

For example, let $X$ denote a smooth manifold. Then there is a ring-theoretic sheaf $R_*$ on $X$ consisting of those smooth partial functions $\mathbb{R} \leftarrow X$ whose preimage is an open set. There is also a module-theoretic sheaf $M_*$ on $X$ consisting of those smooth partial sections of the tangent bundle whose preimage is an open set. With these definitions, $M_*$ is an $R_*$-module.

Answer 1

They're just called $R_{\ast}$-modules, or maybe sheaves of $R_{\ast}$-modules. This is an important and basic notion in algebraic geometry, where $R_{\ast}$ will typically be the structure sheaf $\mathcal{O}_X$ of a scheme $X$.