It is basically the same firmware update and you do need it no matter which laptop you use the disk with. The firmware is the equivalent of the HD's BIOS.
The only issue here is that you HAVE to use the firmware update utility with the laptop that the disk originally came with. This is due to a disk ID that is hardwired.
And, in general, you can use any laptop HD with any laptop. All the way down to some old 2GB disks
