Both .vdw and .vsd files are used in Microsoft Visio, albeit in different versions of the software. Everything points to the fact that vdw to vsd conversion is probably used for reason to use a previously made web drawing (.vdw) in a new or existing document (.vsd). As far as we know, this is only doable with Visio itself and it is unlikely you can achieve this without access to the software.
Updated: September 18, 2023