I'm confused, why are you talking about buying a new drive for the iMac?
Have you failed to mention that it is full as well?
If you're happy with WD, then I would be looking at this -
http://www.wdc.com/en/products/products.aspx?id=210
Depending on which version of iMac you have, you may be able to use the FW800 connection for quicker access and transfer.
As for backing up the current external drive - drag the main folder onto the new drive, and drop. It'll be copied onto it.
You could also use their own backup software provided, but since the current one is full, you'll not be writing to it in order to need incremental updates to the new one.
If the iMac's drive is full, then you'll want to copy the folder with all your photos in it across too.
Regarding the Mac knowing which is which - you decide on what the name of the drive(s) are when you format them, with Journaling enabled.
Lastly, I'd enable the RAID 1 mode on the drive linked, so that when you copy the data over, it writes the same data on the second drive in the enclosure.
You could then wipe the data on the current external (and internal) and using the software provided, set it up for incremental updating.
Having the drives plugged in via their USB/FW cable but not powered on, means they won't be mounted on the desktop, so you could keep the new one off until you need to permit an update scheduled to perform, using the internal or single WD external as your primary storage for new photos taken and edited.
One final consideration is that you could use the Studio II as your backup for the photos, and once verified the photos are all 100% (no corrupt ones), then the current WD could be adopted as your backup drive for Apple's Time Machine, which would take care of the OS, emails, etc, etc, and the internal then being the primary storage for your new photos.