The difference between
/home usually is that the rootfs (including
/usr) has to be mounted early at boot. This is done by initramfs.
On the other hand
/var/www, and other regular partitions you might have, should be mounted later, outside of initramfs, in the course of the regular boot process by the full init system.
So the behavior in mounting can be different in some details.
For example, on my system, the rootfs shows up as
/dev/dm-34 instead of
/dev/mapper/SSD-root. That's simply because the partition is identified by UUID, and the
findfs utility is just implemented differently in initramfs / busybox vs. full system / util-linux:
# busybox findfs UUID=fa15678f-7e7e-4a47-8ed2-7cea7a5d037d
# findfs UUID=fa15678f-7e7e-4a47-8ed2-7cea7a5d037d
This command might just as well return
/dev/SSD/root, depending on how
/dev was populated with device names vs. symlinks. After changing symlink direction
/dev/SSD/root -> /dev/mapper/SSD-root to
/dev/mapper/SSD-root -> /dev/SSD/root, the result is identical:
# busybox findfs UUID="fa15678f-7e7e-4a47-8ed2-7cea7a5d037d"
# findfs UUID="fa15678f-7e7e-4a47-8ed2-7cea7a5d037d"
I haven't looked at the code how it decides which name to pick as the canonical one.
In the end it doesn't really matter, as long as the correct filesystem is mounted, this is at most a cosmetical issue.