Just add the drive into the new computer (if a desktop) and it will show up. Again "files" will be fine. Apps or programs will have to be reinstalled.
And NO. You can't put the old drive into the new PC and boot it. Unlike a tire on a car, the OS will fail and you might damage the files.
So the options are:
1. Put the old drive as a second HDD into the PC.
2. Put the old drive in some USB case to copy your files out.
My old HP running windows 7 died (graphics...HDD is still fine) so I got a new small form factor HP tower running windows 10. How can I get the files off my old HDD? I assume I will need a case to put the old HDD into as an external drive, but will the different OS mess things up? What about pulling the new HDD and just putting my old one inside? Please pretend I am a neophyte and know next to nothing. Thanks!

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