Logical volume management (LVM) is based in:

While LVM manages storage, it operates at a higher level than the raw storage system itself (e.g., a physical disk array or SAN), which merely provides the underlying physical storage.

A virtualized SAN file system is a specific type of storage system or file system, and LVM is a volume management technology that can be used with various underlying storage, not exclusive to or based in a virtualized SAN file system.

Logical volume management (LVM) is typically implemented as a software layer within the operating system of a host server or computer. It allows for flexible allocation and resizing of storage by abstracting the physical disk storage into logical volumes, which are then presented to applications and file systems.

A NAS appliance is a complete network-attached storage system that might internally use LVM, but LVM itself is a component of an operating system, not the appliance as a whole.