I go to a "group" because I generally know the context why everyone else is there. It's usually some shared trait - we are all alumni of the same school, have similar jobs, are parents of similar aged kids, etc. We aren't there because we necessarily share interests (though we might), but because we are all similar enough that questions I'd ask the group would be relevant to most and I'd be likely to get a good answer. Nextdoor is a good example of groups - we all live near each other so it's a good place to post questions to people with similar homes or similar local concerns. FounderDating is the same way - we are all here because we are founders or part of the startup ecosystem.
Forums feel to me to be much more about shared interests. I go to a Seattle Seahawks forum because i like the seahawks. I expect us to talk about that interest in the forum. I don't know if I have anything else in common with the other members, but we at least all share this interest. Same is true for most other forums I'd join. It's about the content there much more than shared attributes of the members.