It will seem an odd question at first, but who made the 80 GB drive?
Reason I ask is, many HDD makers make available for FREE on their websites a set of utilities that do this job perfectly. While they are commonly used to clone an older drive to a new larger one, they can do your job just as well. Seagate has Seagate Disk Wizard, and WD has Acronis True Image WD Edition, both based on Acronis. BUT each version has been customized to make the clone copy TO that maker's drive (they don't care whose older drive you are abandoning). Other HDD makers may have similar free tools.
You download the software and install on your current C: drive. Then you mount and connect the new drive in the machine and run the software. You MUST be sure to identify properly SOURCE and DESTINATION drives because EVERYTHING ON THE DESTINATION DRIVE WILL BE DESTROYED! In fact, since you're re-using an older drive, I suggest you specifically Delete any previous Partition(s) on the 80 GB unit. As you set up options, it often wants to make the clone copy is the same size as the Source (impossible in your case, but the software may figure this out all by itself), but you can manually set to a different size. You will want it to Create a Primary Partition that is bootable, and you may need to select a File System to use. For most new large drive users the choice is NTFS, but you have an older smaller drive. IF your older 90 GB unit is running NTFS, make the clone that way, too. BUT if you have been using a FAT32 File System, you could tell it to do that or try to change it to NTFS if you want. I don't know if that works or not. Run the software to make the clone.
When done, shut down and disconnect the older 90 GB unit, then boot up and adjust the BIOS Setup to boot from the 80 GB unit that has the clone. Verify that it works. Then you can leave it that way, or shut down and re-connect the 90 GB unit and set your BIOS to boot from whichever one you want, but not the other just to avoid confusion.