Discord lacks multi account feature on mobile (some desktop support had come recently). It enforces use my "gamer" profile to all other community. Slack did it well from very beginning.
I have to disagree, I can setup a profile and name per discord. I strongly dislike Slack's method of having different accounts tied to a single email but each can potentially have a different password. I hate having to switch and log out and log into different Slacks and there's no clear way to see an overview of all of the ones I am in efficiently. It feels like a UX thing more than a functionality thing. Discord's UX for managing notifications and what communities I'm part of is very pleasant.
I am only a "gamer" in the gaming related Discords. There's no cross talk between two Discords unless the other people also share in being a part of both communities. People in a music related discord don't ask about the game I am playing unless they happen to be interested in it.