Is Discourse free?
The software is, completely - Discourse is 100% open source and you can self-host it for free on your own server, paying only for the VPS. If you would rather not run the stack, Discourse, Inc. sells managed hosting starting around $100/mo. BuddyNext is also free at its core, but it runs as a WordPress plugin rather than a separate application.
Is BuddyNext a forum like Discourse?
No, and that is the key difference. Discourse is forum-shaped - threaded topics and categories. BuddyNext is social-shaped - an activity feed, member profiles, spaces, and following, more like a social network than a message board. Choose based on how your community actually talks: long-form threads point to Discourse; a social feed points to BuddyNext.
Can I run Discourse inside WordPress?
Not really - Discourse is a separate Ruby on Rails and PostgreSQL application. You can connect it to WordPress with an SSO/embed plugin, but you are running and maintaining two systems. BuddyNext lives inside WordPress as a plugin, sharing the same users, theme, admin, and database, so there is no second stack to operate.
Which has better moderation?
Discourse has the more mature, battle-tested moderation toolkit - trust levels, flagging, and rate limiting refined over years on large public forums. BuddyNext ships a moderation queue free and a rules engine on Pro, which is solid for a community site, but Discourse is the heavyweight here if hardcore forum moderation is your priority.
Can I move from Discourse to BuddyNext?
Both keep data in a place you control when self-hosted, but they are different shapes on different stacks, so this is a real migration, not a one-click import. Threaded forum topics don't map cleanly onto a social feed. Plan it as a project, decide how forum content should live in a social model first, and test on a staging copy.