Discord is a chat software. It has some baby forums.
Discourse is a forum software and it has a baby chat 
Discord is great for real time communication, with no reason to be indexed by search engines. Discord would feel kind of useless without people online.
Discourse is great for long communication, preserving topics that can and should be indexed and discovered by search engines and users. If no-one is there, you can still find a lot of stuff and ask questions. People will answer later.
So it depends what kind of community you want to build. Do you just want to gather around online events or talk? Discord. Do you want to think about whatever your topic is about and discuss it, preserving the answers for anyone looking for the same a few years later? Discourse.
Discourse has a few tons of functionality for moderators to prevent spammers and bad people overall. It can be also customized visually. It’s like a Wordpress for forums.