The notion of the Sith, as an order of evil Force users, was introduced in The Phantom Menace. The name "Sith" is much older, appearing in early screenplays for The Star Wars and first published in the Alan-Dean-Foster-ghostwritten Star Wars novelization. However, in those early appearances, "Lord of the Sith" was an unexplained title. (In fact, the novelization suggests that Darth Vader's appearance may actually be common to all Sith lords.) There was nothing concrete that indicated that there was a Sith order, or that that order necessarily had anything to do with the Force
Prior to The Phantom Menace, as noted in the question, villains attuned to the Dark Side of the Force were frequently described as "dark Jedi," especially in the works of Timothy Zahn, which were the most prominent expanded universe works in the run-up to the release of the first prequel.*
The Phantom Menace also introduced (or at least formalized) the principle that the Sith lords were titled "Darth." This was a cause of some discussion and debate among fans when the character list for the movie was released to the press, because in A New Hope Obi-Wan appears to treat "Darth" as a part of his former student's proper name:
OBI-WAN: You can't win, Darth. If you strike me down, I shall become more powerful than you can possibly imagine.
There was also some discussion, after Episode I hit theaters, of whether a "Sith" and a "dark Jedi" were exactly the same thing. The argument in favor of this proposition was based largely on Qui-Gon's lines from the film. Shortly after the confrontation with Darth Maul:
OBI-WAN: What was it?
QUI-GON: I'm not sure... but he was well trained in the Jedi arts. My guess is he was after the Queen....
Then more prominently later, before the Jedi council:
QUI-GON: He was trained in the Jedi arts. My only conclusion can be that it was a Sith Lord.
KI-ADI: Impossible! The Sith have been extinct for a millennium.
MACE WINDU: I do not believe the Sith could have returned without us knowing.
This suggests that dark Force users (or at least those whose particular skill set—including lightsaber use—closely matches that of the Jedi) are automatically considered Sith. Therefore, it was argued by a number of fans that "dark Jedi" and "Sith" were synonyms. In fact, it turned out that the canonical solution (at least for the prequel trilogy) was to remove the notion of "dark Jedi" from the canon, with the light-aligned Jedi order being the only "Jedi" sensu stricto.
The "Sith race," on the other hand, was entirely a product of expanded universe materials—to the extent that one could watch the movies and essentially never encounter the notion. The supposed Sith home planet was introduced in the 1994 Tales of the Jedi: Dark Lords of the Sith comic book series, which turned out to be inconsistent with many subsequent works. However, the idea of the Sith having originally been a single race has continued along since in a certain train of expanded universe works of dubious canonicity.
*It is possible that the notion of a Sith as an evil order was first introduced in some lesser-known expanded universe material that I am not familiar with. However, it is important to keep in mind that in between the releases of Return of the Jedi and The Phantom Menace, a prodigious number of expanded universe works were released—many of which made only cursory attempts to be consistent with the original three films, and practically no attempt to be consistent with one-another. No one is likely to treat revelations from the Saturday-morning Ewoks cartoon as having any canonical standing, and many of the novels written in this period were thought of the same way. As another example, The Courtship of Princess Leia, although a bestseller, was frequently derided for a treatment of Force users utterly at odds with what had been described in the original films and in Zahn's novels. In any case, George Lucas made it clear that, as he was preparing the prequel trilogy, he was essentially not paying any attention to any facts establish in the various expanded universe sources—so the Sith being an evil order was a new invention (or perhaps something he had long had in mind, however had not included in the original films) for The Phantom Menace.