But yeah, you've definitely got better fonts installed.
Oddly, what you show for your browser screenshot is pretty close to what I see if I select a lucida font, though it's definitely not the font you're showing (adjusting hinting makes it a little better, though not normal). But it only changes my DE fonts (I'm back in xfce) and doesn't touch my browser (firefox). Additionally interesting is that in firefox, I only have the TTF/opentype fonts available, and same with chromium, so I can't make the browser window look like your screenshot.
Yours looks like maybe subpixel rendering is turned off (something that you'd do if you're on a CRT, since they don't benefit from it). Might that have gotten disabled somehow? (again, since I never did anything with it, I assume it's normally on by default...)
Your terminal window looks OK as far as rendering goes, for the most part. It's picked a wider/rounder font than I'm used to reading, not sure if that's the font you want to see, or something else.
If you locate the issue, let us know. It's good to have the solutions up for anyone seeing it later.