If anything the terminology shift was the other way, we called forums and MySpace social media back then even though MySpace is called social networking now. "Networking" back then was pretty restricted to business / self-promotion oriented stuff like LinkedIn.
This is based on changes in trends and is somewhat of a moving target so I'll give some dates.
In the 2000s, 'forums' were forums, and 'social network' was the dominant term for products like FB and Myspace. A movie even came out with that name. Both were also 'communities'. These are verifiable on Google trends.
In the 2010s, 'social media' became the preferred term, mainly because it contrasted with 'the media' as the other major source of information available, but also because it was just an easier to use and more generic term than 'social network'. 'Forums' were still largely forums, tho like all activity online, on occasion it got lumped into 'social media'.
Sometime in the 2010s we started to delineate 'social network' from 'social media' as distinct eras of social products and properties of how the products work. This became extremely clear once the era of video took over in ~2020, as video is historically 'media' in a way that exchanging text never was.
The term 'networking' is/was its own thing and mostly unrelated to 'social networks'.
FWIW I did market analysis for Yahoo's online communities division in 06 and worked on two FB app startups, one which was a college social network, and interfaced a lot with FB in 08-12. All of these words and fine delineations were essential to my work and part of the research I was doing at the time. I looked over my notes to confirm.
I was also there. We (ie the people I interacted with) called myspace social media and considered discussion forums to be a specialized subset of social media.
We also considered myspace to be a social network (due to the friend graph) while forums were not.
The chans were a weird almost edge case. I think they qualify as social media but the lack of persistent identities significantly changes the dynamics (obviously).
As far as I know chans are always considered "image boards" and they are usually distinct by the fact that the information is "pushed off" the board after a time or amount posted afterwards.
