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.
Once you change the password, it has been charged and the old password can not access the FileVault decryption protocol. It would be nightmarish if you had to always remember any and all passwords ever used by the FileVault account(s).
If you want really great info to FileVault please watch: http://docs.macsysadmin.se/2013/video/Day2Session5.mp4
Best Answer
I'm afraid there are not many options given an ordinary, "home user" budget.
Theoretically you could send the drive in to a recovery service such as IBAS to get them to recover the original data on the drive. If this is even remotely possible depends on what kind of physical medium you had (i.e. is it SSD or spinning-platter hard drive). If they can recover everything, you can use the standard Apple tools to access the encrypted drive with your password or recovery key.
If you can't recover the full data set, you would have to inspect the data manually and probably create new tools for decrypting blocks of data using your recovery key. This will require specialized knowledge and skills, considerable amount of time - and with no guarantee of success. It is out of range for ordinary, home user purposes. FileVault 2 uses AES-XTS encryption - if you haven't got the recovery key and/or volume master key it is going to very hard (next to impossible) to decrypt.