Filevault's use the XTS-AES 128 encryption. As Finder's contextual menu encryptation option and the Erase with the Encrypted format use Filevault's system, the encryption is the same.
Disk Utility's, in the other hand, when creating an new image, lets you choose between a 128 or 256 bits AES Encryption.
These two methods are, therefore, different. The latter just creates a folder which requires a password to be opened, while Filevault is a lot more complex.
And for the Logical Partition, here is explained in detail.
How Does FileVault 2 Work?
Compared to the bare file system, or even FileVault 1, FileVault 2 seems like magic. How does it work? The first thing to know is that Apple has included a Logical Volume Manager (LVM) with OS X Lion. This is what FileVault 2 gets to ride on top of. 
Physical media still exists—we really can’t get away from that, as the data need to be stored somewhere. CoreStorage doesn’t really care what the media is, though: traditional spinning-plater drives, SSD, USB storage or even a disk image. Represented above in green, we have three volumes that reside on some physical disks. These three volumes are converted into CoreStorage volumes and imported into a Logical Volume Group (LVG). This sets up a “pool” of storage. Volumes can be added to and removed from the pool after creation. A LVG is represented with a UUID. This LVG is then brought into a Logical Volume Family (LVF). An LVF maintains properties about the volumes in a LVG and presents these Logical Volumes (LV) to the system. CoreStorage creates new device nodes for each LV. As shown in the visualization above, the LVs, in blue, have a device node (disk1, disk2, disk3). The ‘key’ icon associated with the LVF shows that encryption is one of the properties maintained about the LVG. This is the layer at which the encryption key resides.
When you “Turn On FileVault…”, one of the steps converts your disk to a CoreStorage volume. Of course, when you “Turn On FileVault…”, only your boot disk is encrypted. Naturally, this fits Apple’s 99% case and is the right fit for the bulk of Mac users on the planet. That said, FileVault cannot and will not encrypt any other drives you may have attached to your system. That’s up to you.
Boot into Recovery HD, open Disk Utility. Choose Yo Drive in the list and select the Restore tab. Make Yo Drive the Source and Macintosh HD the Destination. This will erase all content on Macintosh HD and replace it with the contents of Yo Drive. Back up anything important on Yo Drive before hand in case of failure during the restore. After that you should be able to erase the second partition and extend to take up the whole drive.
Best Answer
I think the most secure way is to use
diskutil zerodiskand then follow up with either command. Both of those commands remove the reference to logical structure on the disk but a good file recovery tool would still be able to recover most material on the unstructured volume by matching file templates to successive sets of bits. You want to write over everything with 0s or garbage before you dereference the volume.UPDATE: It was negligent of me not to mention that
diskutil secureErasealso exists and it combines the two commands with options for multiple passes of zeroing the disk.