Well the pic you show is most definitely FireWire, simplest way to describe it is think of a USB port, now shape 1 end so it is close to being a semi circle, except it has 2 flat corners as opposed to an actual curve, but assuming I have found you're device, it has the most connection options I have ever seen, it has what it calls a quad interface, so from what I can see you have 4 possible connection types available to you, this means if the system you connect to has the appropriate connection, the external drive can take advantage of a much faster connection by using a different port, here is what they say:-
Quad interface - Power your creativity with connections for ultra-fast eSATA and FireWire 800. For flexibility and convenience, FireWire 400 and USB 2.0 are also included.
This is what came up in a search of the model you gave, if this is right then what you have is 2x1TB drives in raid0, so it will appear as a single 2TB drive, this gives you speed, and is the default setting when you get it, BUT, you can change this to raid1, this will halve you're drive size down to 1TB, and the benefit of raid1 is it's a mirrored array, in raid0 if one of the drives goes faulty, then thats everything gone, you can't retrieve data from a single drive as it's spread between the 2 drives, and as such has the risk of losing the data if the worst happened.
With a mirrored (raid1) array you get 2 drives with identical data, so if one drive dies, the other drive has a carbon copy of the data, so if what you're using this for is essential data, a raid1 array is a must.
Now the important thing is to use the right cable with the right port, eSATA is the fastest connection, and if the PC you connect too has eSATA then that is the best connection type to use.
The unit appears to come with all the cables, all except the eSATA one anyway, that cable comes with the system or card for the system as far as I know, and you drive has 2 FireWire cables, and 2 ports as well, the difference is one is half the speed of the other, so if your using the 400 port, you should use the 400 cable, same with the 800 port, otherwise you wont get the max from it, but
go Here and it should help explain the difference in each.
As to if your new PC can take any of these formats, you will need to check the documentation that came with it, if you have a make\model for the new system I can try and see what it has available to you, needless to say do NOT jam in any old cable until you have clearly identified which port does what, hope this helps a bit.