They are totally different, but same at same time. USA and UK are problematic because those countries have ancient legislation system where judges can create laws — I blaim their grain based measurement over logical metric system 
But in generally forums doesn’t matter here. Platform per se means nothing and it is just matter of copyright of content. So there isn’t any law cases about forums and public domain (disclaimer: in the States is law cases about anything and rules and restrictions depends per county, state and federal 
) because public domain is just another lisencing system. If an user gives publishing rights away (mostly falsed called as copyright), aka. public domain, it doens’t ask if it happends on forum, website, social media platform or paper book. It is just matter of content.
Sure out there is tons of law cases because of copyright violations — photos, music, videos and games are perhaps the most familiar ones. But again: it depends of agreement, T&C. If a creator knows for sure that publishing platform is public domain there is no place for legal cases.
Here on Meta is a lot of content that is public domain. I’m a typical user and I never red T&C here, but rights are given away by company or creator telling this is free for use and copying.
And most of content of forums (or on social media) aren’t works that would have any copyrights at all. Yours question and my answer are such.