Social Media is a word that means less than the sum of its parts. It is not just the word Media modified by being Social; it was invented to describe algorithmic feeds like Facebook and Twitter. Discord is not social media. Discord is a forum, a type of thing that existed before social media.
Social Media's organizational principle is the user page, while Forums are organized by community and discussion topic. Reddit is also not social media, despite having some algorithmic features, because it is organized by community/thread, not by social network. You go to a subreddit to read the posts there, not to a user page to follow them.
what you describe is not the definition of social media which I see commonly used, especially in a legal context
technical details like weather it uses threads in the end IMHO doesn't matter for weather is social medi
social media is internet media used is used for socializing
which means that while classical forums are most times not social media but they can be
discord is not a form, it gained forum functionality somewhat recently, but the most common use case people have for discord is to socialize, hangout and chat in small communities. Does't mean it doesn't also get used as a forum, still it's more used for social interactions then anything else.
Reddit on the other hand is in between a classical forum and social media, though increasingly more social media in recent years and saying it's not social media just IMHO isn't right.
So you think that even IRC and text messages on your phone are social media? Can't agree. Being a chat room is not enough. The social in "social media" stands for social network, not just any kind of social interaction at all. The key innovation with social media is using technology to leverage your social network for discovery and recommendation systems. You can't have social media without a social network platform through which it gets distributed.
EDIT: On reflection, the key point is that social media is an alternative to traditional media, like newspapers and magazines. The term refers to a way of publishing and distributing content. So I change my position that Reddit is indeed part of social media, not because you socialize on it, but because it is a platform primarily used for publishing/distributing content. Places where you just hang out with your friends on the internet are not content distribution platforms, however. (Unless the only interaction you have with your friends is sharing and discussing internet media.)
I propose this definition: Social Media is the practice of leveraging social network and community platforms to publish and distribute media.
While communication platforms like Discord might get roped into the social media ecosystem, sharing liking and subscribing is not its primary purpose. For something like Reddit and HN, it's easier to say that media distribution is the primary purpose, but not 100%. Going a step further, platforms like Youtube and Twitter are used for both publishing and distribution, so they're not just communication platforms, they're the end-to-end social media platforms.
Social Media's organizational principle is the user page, while Forums are organized by community and discussion topic. Reddit is also not social media, despite having some algorithmic features, because it is organized by community/thread, not by social network. You go to a subreddit to read the posts there, not to a user page to follow them.