Nope, definitely not. There is just ONE partition, and it takes up the entire drive. I can click on either icon and get full access to all the contents of my drive. Furthermore, ejecting just one of the "icons" doesn't prevent me from using the other, which stays nicely well-behaved on the desktop. (For tidiness reasons, I usually do just go ahead and "eject" the second copy whenever I connect this drive - doing that doesn't seem to affect the use of the first icon.)
So this is a bit of a mystery, then?
One possibly relevant detail is that the external enclosure (2.5") has two firewire ports. I can't remember why, but it was a selling feature of the enclosure at the time I bought it (a couple of years ago now). Something to do with being able to connect the enclosure to two Macs at the same time. So perhaps this is some oddity of the enclosure.