Those screenshots were both in Waterfox. I also tried in Safari (didn't take any shots, though) and the fonts looked identically bad in that browser as well.

The normal UI's fonts are also worse -- about the same as the browser screenshots. Fonts are indistinct and blurry, and very light. All the result of greyscale aliasing only, I presume.

Either Apple disable "LCD font smoothing" for retina displays, or there is a bug somewhere. Because in Mojave on a non retina screen "LCD font smoothing" has got the same weight as before. And on your screen it clearly doesn't.

I hope it is a bug. If the weight were the same, it'd at least perhaps be tolerable on a Retina screen. I know the technical reasons, but I just don't understand why Apple can't leave it alone for desktop systems.