I try to answer this based on my experience, but I don't have any other source.
- Favorite tags
- Don't aggregate more question of that type
- Change only the background of questions with that tag (if you did not search for them).
- Ignored tags
- Are removed client-side (with JS)
- Just don't display.
Questions that have both ignored and favorited tags are ignored (I once ignored ns2 because it appears mostly with my favorite tag tcl, but I don't have the nessecary domain knowledge to answer most of them.)
I have a set of low-volume tags as favorites, so I only see a single question with a sqlite on stackoverflow.com.