Barracuda = 7200RPM, Desktop oriented part.
Cheetah = 10K/15K RPM, High performance - Server oriented part.
Momentus = 5400/7200RPM , Low Power - Notebook oriented part.
In other words, all the 7200RPM Seagate disks intended for Desktops are effectively known as Barracudas, irrespective of the model number.
You need not worry about models , 7200.8 series covers only the higher capacities - 200GB onwards ! You can rest assured your 80GB disk will be a 7200.7 model.
Even so if you need to check, the model number for a 7200.7 80GB PATA disk will be : ST380011A or ST380013A . You can confirm this with any of the dealers you ring up , they'll be happy to tell you these model numbers.
EDIT: Silly Me ! Dint see the date of the post, I guess you would have your HDD by now!
Nonetheless, hope the info is useful.