A vector space is simple a module over a field as opposed to an arbitrary ring. But, there are times, for example when $R=D$ a division ring where we refer to a module as a vector space. For instance, $M_n(D)$ as a vector space of dimension $n^2$ over $D$. However, this clearly would not satisfy the definition of a vector space for an arbitrary division ring since the scalar addition may not necessarily be commutative.
In instances such as these, are authors just abusing notation and really just mean a free module? To generalize the example above, $M_n(R)$ for an arbitrary ring is of dimension $n^2$ over $R$ and, hence, is a free object over (which acts on another free module $R^n$) $R$.