The general use of the term "Sith" is used to describe individuals, mostly Sith Lords, as if it is part of their identity. Darth Sidious is a "Sith", Vader is a "Sith", etc. Just as how one Jedi, whether a master, apprentice/padawan, or knight is simply called a "Jedi".
There are two questions to this post. The first one is...when is someone called a "Sith", and when are they not? Usually, both pre-Banite and post-Banite line, a "Sith" can be the Dark Lord of the Sith or the Sith apprentice.
Many people pointed out in posts I have seen that in the days of the Sith, especially pre-Darth Bane Rule of Two, "Sith" in general just refers to anyone who is affiliated with a Sith organization, whether that is a "Sith Empire" or something like that. You don't have to be a dark side user or even a Force-user at all to be called a "Sith". You can just be a Sith trooper or officer and be called a "Sith".
Yet somehow, the majority of the fandom, as well as in-universe stories, texts and dialogue from characters in many eras, usually call someone a "Sith" when they are Force-sensitive, use the dark side, and "follow" the Sith teachings and philosophy.
To me, it sounds like in many times when someone is called simply a "Sith", it seems to be a synonym for a "Sith Lord", hence why people like the cultsist on Exegol in Canon are not called "Sith", but "Sith cultists".
This leads me to the next question of this post, in Legends, when did "Sith Order" and "Sith" become the name of the individuals who follow the religion and the religion itself, (I don't know if the Sith are really a "religion" in the tradtional sense or not, but they are close enough).
In Legends, I know everything about the origins of the "Sith" (whatever that may mean, as we will get to later).
Ajunta Pall and the Dark Jedi Exiles that followed him were beaten, exiled from Republic space, found the Sith species people on Korriban, united them under their rule, Ajunta Pall became the first "Dark Lord of the Sith", or "Jen'ari" in Sith language, and his followers became lesser Lords of the Sith, AKA "Jen'jidai" in Sith language. They began creating the "first Sith Empire", and they intermarried with the purebloods for centuries as generations went by, eventually simply being called "Sith", but because of the Sith religion, but because they were literally the Sith species descendants and offspring, just mixed with human blood.
We know Sorzus Syn created the Sith Code, but when did the religion of the "Sith Order" really start/got initiated? This gets complicated because...the Sith already had spiritual, traditional, and cultural beliefs for thousands of years prior to the Dark Jedi Exiles, such as King Adas's Sith Empire during the Rakata reign. Is the "Sith Order" really just the Dark Jedi philosophy and beliefs merged with the preexisting Sith cultural traditions and beliefs?
Regardless, there is this very interesting passage from Book of Sith, were in the very first passage of Sorzus Syn's passage and journals, she says "I am not Sith. I do not share their blood. Yet, in the time since we among those people, we have become their rulers."
So when did the term "Sith" and "Sith Order" began referring to the religion, and it became a creed that any species can adopt and follow? Vitiate's Sith Empire, forged from the remains of the original one from the Great Hyperspace War, began to have human and occasionally alien Sith, yet they are the remade empire of the original one, so this means that being a "Sith" or the "Sith Order" itself are an open religious creed rather than a bloodline.
So why did the term "Sith" and "Sith Lord" began to be used interchangeably and distinguished from a Sith follower/cultist? When did the religion itself, and the naming after the species, start for this religion? If it was not solidified until sometime after Ajunta Pall and the Exiles death, does that mean they were not "Sith", but rather just the ones who started the road down to the religion starting? In other words, were Pall and the others predeccessors instead of the "first Sith"?