Proper color filters would only work on the image on the way to the video card, and not affect what other software sees. E.g. Flux works this way in MacOS, and, I think, Windows.
The difference is probably due to the application of color profiles in one of the programs.
hat being said, yeah, using the color picker on the screen gives different results.
In my case, that's because I shift my screens towards the red to avoid blue light exposure.