Slice of Life stories usually have drama associated with them. And in our country(And probably around the world, from what I've seen), most of the published slice of life stories are SoL Drama... So, usually, there isn't much distinction between them to most people.
I personally view SoL as literally slices of life. An action story might involve SoL elements, and a mystery story might slap me out of nowhere with some good SoL... And that's what SoL kind of is to me. Me seeing other people's lives. In slices. I enjoy SoL way too much probably. It's, in my opinion, what breathes life into the characters in a story.
Drama is just drama.... Moments of elevated emotions and stakes and that may be in any genre, I think. SoL- Drama stories get bland fast sometimes with how melodramatic it can get, or how same-y it becomes. But a well-done Slice of Life story has all the sides of life... the happy moments, the sad ones, and the dramatic ones. And as in real life, dramatic moments should be few and far between imo, unless that's the intention.
