To make your life simplest and involve the fewest headaches, you should indeed just swap the drives. Take the cover off both your old and new 8500. It's one or two screws at the back, then slides forward and up(watch the plastic!)
You should see the hard drive from the front of the computer-it will probably be right under the CD-ROM drive.
The drive will be mounted on a white-ish plastic sled with a tab on the front. Push the tab up then pull the drive out about a 1/2" or so-you should feel it hit a stop. From there, you can lift the drive straight up and it will be "free" from the attachment to the computer case.
Once the drive is free, you will need to unplug the 50-pin ribbon cable from the back along with the 4-pin power connector. The power connector can be a real bear, especially since it likely hasn't been out in 15 or 20 years. Hold it by the sides and "rock" it back and forth while pulling-it will eventually come loose.
Once the drives are free from both computers, you can reverse it to install the old drive in your "new" computer. Make sure the ribbon cable is fully seated, and then hit the power button(I'd suggest on the keyboard) while you still have the computer apart. It should chime and you should be rewarded with a desktop that's just like your "old" computer.
If you want more storage space, it IS possible to put both the drive from the "old" computer and the "new" one in, but that will require a bit more work. If you're going to do that, please come here and ask. It's not overly complicated, but at the same time you will have to change a couple of jumpers(the small plastic blocks on metal pins) on one of the drives. Otherwise, you will likely end up with neither drive being recognized. For a more technical explanation-all the drives on the 8500(HDD, CD, Zip) are on a "SCSI" bus. A SCSI bus of the type in an 8500 supports 7 devices, although one of those devices is the SCSI controller on the computer. Also, SCSI devices are on a continuous "chain" via the ribbon cable in the computer(and the external devices, if you have any). Each end of the chain must be "terminated." Each device also has an ID number-from 0 to 6-that uniquely identifies it on the bus. For a 90s Mac, the CD drive is normally ID 3 and the boot drive is ID 0. Also, the boot drive is at the end of the chain, so it is terminated(the computer terminates the other end). If you put the drives from both computers in, you will end up with two drives at ID 0 and termination on-and the computer can't read either. The fix is to change one to ID 1 and turn termination off-then everything will work fine.
All of that aside, you should have no issues just doing a straight swap of the drives. Just be careful with the plastic!