For forums, in the conventional async sense, your big options are :
PhpBB is the old, venerable, ancient but-still-open-source option. It's not pretty, it's not nice, and it's not getting a bunch of new updates on a monthly basis, but it's been around long enough to drink.
vBulletin is the paid software equivalent. Not worth it, imo, but it did have a major following... over a decade ago.
XenForo is the middle-ground. Very Web1.0 styled, with newer backend support and a faster development pace.
Discourse is the 'newest'-looking and most divergent mainstream forum software. It's wildly different in appearance and heavily Web2.0-styled, to the point of kidnapping CTRL+F, but it does have a lot of nice design decisions with the bad ones. Upside, lead by a StackOverflow guy. Downside, lead by a StackOverflow guy.
For less mainstream options:
If you're willing to put in the effort, Lemmy, Tildes, and Lotide/Hoot kinda work for small groups. They're weird and very opinionated, and performance isn't great, but you get a much more modern setup.
The drama website itself has a ton of bizarre and often-anti-human UI decisions, but the codebase is pretty respectable, and there's some less opinionated and more pretty forks out there. Gets you a modern backend and magic like unit tests and type annotations, like you're a real programmer... which only helps if you want to program anything.
RocketChat is the easiest to setup option I've evaluated. It's also the most commercial software (technically: open core, paid feature licenses), and they've cut down on their free-tier over the years. At this point you can't get voice chat or long history without paying for it. Whether that's a problem for you depends heavily on your use-case.
Mattermost is slightly better, but it's a similar boat: open core, paid licenses. The free version's better-featured, with free voice chats (supposedly going to be limited to 40 minutes in a future release). In exchange, the UI is a little more Slack-like than Discord-like.
Stoat/Revolt is the explicitly-trying-to-replace Discord chat, focused on text and voice. It's pretty powerful and very Discord-like, but despite being around for five years it's still got some rough edges and always seemed a little seat-of-the-pants.
Matrix (technically, any Matrix-compatible server; Conduit is the one I got running, with Element as the client I used most) is the hardcore techie one. It's the most powerful and its handling of privacy/encryption/federation is the strongest and it has strong support for chat/voice/history, but it's not a great user experience as a result.
Zulip kinda does both text chat and forums, but it's very topic-focused, even compared to the already-topic-focused Discourse. While it claims to have voice chat support, it's just letting you link into a handful of third-party (and mostly commercial) providers. Not great as a Discord replacement imo, but for some uses it makes a lot of sense.
NextCloud is a file share first, but it does have a surprisingly full-featured text and voice chats. More attempting to mimic pre-MicroSoft Skype than Discord, so chats are more organized by people than by topic, but performance is good and if you're using it as a file share already, it can be easier to set up than almost any alternative. No forum feature, though (they use Discourse for their official forums).
Mumble/Murmur is a voice chat program first, intended as a Ventrillo/TeamSpeak competitor. It does have text chat support, but no history -- I'd really only recommend it as a supplement to a separate forum/chat service. That said, it is really good as a voice chat; I've used it professionally, and a good few major games use it as their internal voice service.
XMPP is a protocol, and the featureset supported depends heavily on implementation and configuration. I can't recommend it because the ecosystem is so fragmented, but I'll mention it because it does exist and does do everything... just with a big asterisk of 'when supported by the server and client'.
IRC does techically have a chat history backend as of IRCv3.