I'm curious, does the EU have an equivalent to section 230? Or do they already operate in the way that a post-230 US would?
Varies dramatically. The EU is not really the equivalent of the federal government in the US, though they do make legislation that all EU members (the UK being in the process of leaving, not all things in geographical Europe being in the EU) agree to integrate into their laws and follow over the coming years, each state (and sometimes subdivisions of them) still have enormous autonomy.
You might have heard it in context of article 13 a few years ago
https://www.wired.co.uk/article/wha...ean-directive-on-copyright-explained-meme-ban and
https://www.bbc.com/news/technology-51240785 (UK not implementing it).
Anyway beyond that then the distinction is not really made the same way. For the UK then each field tends to have its own thing, own regulatory body and rules set by which they get to operate. Most of it antiquated and not really dealing with this internet lark so well.
Broadcasters, some telecoms, postal services (though most of that is in turn farmed out to the postal providers themselves)
https://www.ofcom.org.uk/tv-radio-and-on-demand/broadcast-codes/broadcast-code
https://www.ofcom.org.uk/phones-telecoms-and-internet/information-for-industry/codes-of-practice
https://www.ofcom.org.uk/postal-services/advice
Newspapers
https://www.ipso.co.uk/ though they are dubious in the eyes of some (toothless or in the pocket of).
https://www.impress.press/ is a newer one that various press industry panels recognise but only a few more local types use it
Advertisers
https://www.asa.org.uk/
On the internet this also gets tricky.
Social media regulation...
Slightly under ofcom but more is likely to come
https://commonslibrary.parliament.uk/research-briefings/cbp-8743/
What legal potency each of those had varies, though fines, regulations being looked at it courts and more besides do come from them. You are way more likely to hear of cases involving them though than some kind of police force or national crime agencies starting a case, or an internet company citing it as a defence in court (or trying to adopt the best position around that for the given case in court). Generally it is recognised that you probably don't want mega fines for having a comments section so most of those will have phrases like "expeditious removal" to mean the same thing as timely removal in response to properly filed/served legal notice.
Rinse and repeat for every other country, some of which do things quite differently (we had a few posts around here about Germany's censorship practices vis a vis games, though that might not be quite the same thing even if the law underpinning it tends to inform what others do).