Slice-of-life (for me anyway), is just following the life of a single or set of characters. What happens to them doesn't necessarily have to be dramatic/funny/tragic/romantic/or anything, but it shows you a little more about the character(s) and who they are as a person.
For example, I categorize my comic Demon House as SoL because it follows the main character's final year of college. Sure she has to deal with supernatural forces, but the series is mostly about her relationship with the demons and her friends. Usually I write funny scenarios or jokes in (because that's how I write) but a lot of times, it's just her hanging out with another character and seeing how their relationship (non-romantic) unfolds.
Anyway, I think a lot of comedic SoL comics are listed as such because many are autobiographical, and these funny things just happen to the author. You see how they deal with said situations and you learn more about them personally, like a friend.
As for what defines a drama, well, it has to have drama I guess? lol. Drama as in the characters are very emotionally invested in something and its high stakes all around. It's an emotional roller-coaster.