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.
SSD is different, it needs a separate driver from OS to work properly. It is better that you archive your drive using time machine, install OS X as usual and than, during the last install step, restore your home directory. This will ensure that your system uses all correct drivers and your SSD will live a healthier life.
When archiving with time machine, you can drag /System into the exclusion list to avoid archiving OS X itself (you'll be reinstalling it).
Best Answer
Secure Empty Trash and FileVault are two different methods for protecting data. FileVault encrypts everything on the hard drive. Only someone with an admin password can decrypt them. This includes anything in your Trash. So by default, the files you delete when FileVault is on are safe via encryption. Even if someone recovered them, they'd still need your password to decrypt.
Secure Empty Trash has nothing to do with encryption. The default Empty Trash just deletes pointers to old files and marks the space they were using on the hard drive as free to use in the future. However, the files are still there if someone ran a data recovery tool or until the OS decides to put a new file over them. Secure Empty Trash prevents recovering deleted files by writing data (zeros) over the space the files you're deleting were using. Meaning the files are completely destroyed.
Here's how it breaks down:
FileVault On | Empty Trash (non-secure) | Someone can still recover those files, but they will recover files that are encrypted per FileVault
FileVault On | Secure Empty Trash | No one can recover the files, so it doesn't matter whether they were encrypted or not to begin with.
Do you need to use Secure Empty Trash with FileVault on? I think it's overkill unless you're afraid that someone will recover files and have your password ready for decryption.