I think Discord is more like slack in that in lends itself more to less formal synchronous chat. However, all these can be used asynchronously, so they do overlap.
I feel synchronous communication (chat) can be good for improving relationships.
I really like the summary emails Discourse sends out – to me, Discourse is still the best platform for concise, useful reference information. Slack and Discord are better for information chat, brainstorming, etc.
I’ve still not used Matrix much yet.
Here is an interesting discussion on this topic: