Vector space versus Free module

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 $$R^n$$) $$R$$.