Based on how I use the two, I'd say - for me - the difference is the time-value of the information.
The forums I actively use have information that is relevant even 5 years after posting, occasionally longer.
The groups I actively use have information that is well out of date even a year later - in the extreme case (mostly social), it can be out of date in a week. Increasingly, Slack is starting to edge out email for me when the time value is lower.
I don't use much that is in between. For the forums, I heavily use search & the web. For the groups, I heavily use email & filters.
In terms of product, I see a trend in becoming more extreme: Slack groups are replacing email groups for me wherever the information value is closer to real-time. I expect a "meta-forum" (forum with no original content but highly specialized search/browse ability across a lot of information sources) would definitely be helpful for longer-lived information: even now, I'm as likely to use Google to find info on SO as I am to search SO directly. However, in a page worth of Google search where I end up on SO, easily half the original items are often irrelevant.
In context of FD, I'd appreciate a "local" FD group that had more real-time info. Most of FD has advice that is as applicable 3 years ago as it is today. In contrast, I saw someone get moderated this morning for posting info on a new co-working space in East Cambridge they are trying to open.
Irrelevant info for the vast majority of people on this forum. However, if you live in Boston, it's actually slightly interesting to know about for next 1-3 months, and could have lead to a worthwhile discussion if the participants were mostly local.
Moderating the post was the right choice given how FD is setup right now, but I can imagine a different setup biased towards more temporary info where a post like that would be encouraged instead of viewed as spam.