Social Network as a term is woefully broad. If you look at the Platforms and Sites entry here, you will see a range of different sites, all with their own approach to things.
In order to not just look at Features and Capabilities, because those don't tell you how such sites want to be engaged with, let us break down things in another way first.
Realtime is the discussion we have at the breakfast table, or when we trashtalk our opponents inside a videogame, in a meeting, over the phone or even text or video chats. The key element is that it happens in real time, attendance is perceived and people generally consider it rude if you make them wait for an answer too long.
Asynchronous communication is much more robust in regard to time constraints. In olden times, we simply knew that the messenger pigeon will take a while to deliver that missive to the King, so we waited. Letters took their time, and it was acknowledged that the recipient will then need time and effort to compose a proper answer.
Senders & Audiences
One to One is a discussion with just two participants. That can be realtime (a phone call) or asynchronous (a letter).
One to Many used to be the prerogative of official proclamations, public speeches and, later, newspapers and radio or tv broadcasts.
Many to Many is something that we have quite a lot today on the Internet. A group of people communicating within itself, or with another group of people. Sometimes in there, you have a few separate one‐to‐one conversations. Sometimes everyone is listening to just one person, sometimes everyone is broadcasting at once while no one listens.
Closed communications strive to be private — no one outside the elected circle may listen in — or they may listen in, but they are not allowed to participate.
Open on the other hand is there for all to see, hear and join.
Posts, Comments, oh my
There is a distinct difference between a webforum, a Facebook-like Social Network and Twitter. And that just doesn't apply who owns and controls the platform, or the user interface, but the underlying messaging model.
Utterances, The Twitter model
(Note the term "Utterances" is a spur-of-the-moment label. It might not be too appropriate in the long run)
Platforms like Twitter or Mastodon rely on a model that treats everything the same way: An immutable Utterance that may be somehow connected to another, but otherwise stands on its own.
You usually cannot prevent others from referencing you or your own Utterances (unless you block them wholesale, but even that is not always possible). This is a very egalitarian model, but it can have a tendency to break down under abuse. It also often makes it hard to keep track of complex discussion as the link-chain between Utterances get confused or break down.
Posts & Comments
A lot of other platforms use this model. In this, one person creates an initial post and then people attach comments on this. These comments can sometimes be threaded, meaning that other comments reference to another comment instead of directly to the initial post. The assumption is that this grouping helps keep complex discussions and their sub-threads organized. Weblogs introduce a third concept to this: Pingback Notifications are short server-to-server messages that attach a notice to another blogpost that it has been referenced by a Post on a completely different blog.
Content Ownership & Control
This is not about copyright, but about who has the ability to edit or even remove an utterance, post, comment or pingback. This is becomes important when things escalate beyond the level of a simple argument, for legal requirements or when abuse, harassment and spam comes into play.
- The author of an Utterance in the Twitter model is the sole owner of it and unless the platform owner does something, it cannot be removed unless the owner wishes so. It is up to the owner to decide who is allowed to see it and what or who is referenced by it.
- The same applies for a Post
- Comments are dealt differently depending on platform - a lot of Social Networks and Blogs give the Post-Owner also control over Comments. Forum Software often defers to the Platform owner, but sometimes also allows the Post-Owner control over the comments.
- Pingbacks are a special beast: The Post-Owner can remove the Pingback reference on their post, but they cannot remove it from the pinging Weblog.
An eclectic set of definitions, guides, and references of not-yet-fully-vetted relevance.
- Social media -- Wikipedia article.
- Things we Need to Talk About: Risk -- Edward Morbius at Diaspora.
- Trey Harris’s Google+ alternatives feature support -- spreadsheet (Google Sheet)
- Social Network Comparison Table -- A similar spreadsheet created by JollyOrc (Google Sheet)
- "High (but basic) Level Analysis of Social Networks and the G+ Predicament" (Internet Archive) -- A classification by Jesse Covner at Google+.
- Types of Social Media -- A run-down of social media types, 5 classifications.
- Different types of social media -- A 7-type model.
- 23 Types of Social Media Sites -- A fairly exhaustive and reasonably good breakdown, as such numbered lists go.