As you have correctly stated,
they just happen to share a name but are entirely different.
Virtualized hardware is perceived by the software as being indistinguishable from the actual hardware. It has exactly the same architecture, down to a quite low level, at which the abstraction layer of the virtualization is crossed.
This is not at all the goal of a VM for a managed language, which creates a virtual environment specific to that language, and identical on all hardware platforms.