fdisk -l shows the PC-style partitions on each disk.
cat /proc/partitions shows the available block devices. sda, sdb and so on are hard disks. sda1 and such are partitions on these disks. dm-0 and so on are LVM logical volumes.
pvs or pvdisplay reports the volumes that are LVM physical volumes.
df shows the mounted filesystems. If a filesystem is mounted from some place like /dev/sda1, it's not on an LVM volume. If it's mounted from /dev/mapper/group-logical, it's on an LVM volume.