Why does Disk Utility show one "Macintosh HD" as a logical drive and another that says core storage physical volume
[Edited to reflect screen shots]

Technically that is 1 Hard Drive and 4 partitions (see how they are all indented from the drive they are in).

It looks like someone enabled showing all volume types in your Disk utility so it's showing you things not normally shown in the GUI.

OS X has something like LVM so you are seeing the Logical Volume (LV) and the CoreStorage (PV) both shown as partitions in Disk Utility. LVM provides many advantages over using a regular partition none of which are assessable in the OS X GUI, but you can read more about it on that link if you are interested. In Linux disks, logical volums, etc are labeled different from eachother but on OS X a disk can be /dev/disk0 and a LV can be /dev/disk1 which can be confusing because they are different in many ways.

Normaly you can only see the partitions that don't directly contain data by  opening Terminal.app running diskutil list.

So you may want to disable that setting to put the GUI back to it's simple defaults.