In a default installation, your disk is divided into two parts at a high level: root filesystem and LVM pool for VM storage.
They both live on the same physical disk. They are both backed by LVM volume group.
Again, as part of the default installation, there are two PVE storage pools: local and local-lvm.
Local is a Directory type storage pool. It points to a directory in the Root Filesystem.
Local-LVM is a separate LVM pool.
Local being full coincides with your Root Filesystem being full. If you run "df -h" you will see a confirmation. You should not run your Root Filesystem at 100%, or even 90%. There will be unpredictable and strange behavior in the OS, and data loss/corruption is possible.
Hope it helps.
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