Do installed stuff leave data on the computer??

For example, I installed a program that had a glitchy file, so I uninstalled that, and used a second version that was supposedly clean and it had the exact same problems.

But I moved to a new laptop, and it's like a clean slate. I went straight to the second version and it worked perfectly.

Another time is where I have a controller that worked perfectly, then I calibrated it and messed up the entire thing. So I uninstall it, checked off "remove all software data" and then I plugged it back in, reinstalled it, and guess what? Those messed up calibrated settings are there without me touching anything at all!!

Is there something that remembers previous versions of the same thing??