It is confirmed that Black Citadel and the Black Temple are one and the same. As explanation, it has been previously stated that Magtheridon ruled Outland from the "Black Citadel," his seat of power where he eventually would be confronted by Illidan (see sources below). The linked article specifically states that Illidan confronted Magtheridon at the "Black Temple," which clearly indicates the two are the same place, and furthermore indicates that Magtheridon was then taken to Hellfire Citadel, clearly indicating that as a separate location.
The remainder of this article deals with resolving the many conflicts and possible retcons involved with letting those two names refer to the same location, as well as to chronicle the history of the temple, and the history of its locations.
In Warcraft III: The Frozen Throne, the building from which Magtheridon ruled was called the Black Citadel and was positioned north of "Shadowmoon Ruins" near the "Mountains of Flame" in northern Hellfire Peninsula on map of Outland. With the new map of Outland, it is now called Black Temple and has been moved to Shadowmoon Valley (south of Hellfire Peninsula).
While the TFT map has a contradiction with the earliest map of Draenor seen in Warcraft II, such as the fact that all Shadowmoon holdings were located south of Hellfire Peninsula in those maps; Black Citadel was never mentioned in previous games (its first appearance was said to be in Hellfire Peninsula). Yet the position of the Black Temple is exactly the same as Shadowmoon Forteress in the first Draenor map, back in Warcraft 2.
It is most likely that the Burning Crusade map was designed specifically in order to make it closer (though not exactly the same) to the Warcraft II maps, the Shadowmoon Ruins on the TFT map were likely moved to the southern peninsula to its original location. However it is unclear why the Citadel/Temple was moved south, and no explanation has been given.
The Temple is now the seat of power in Shadowmoon Valley. It is possible that the "Black Citadel" was what the people around Shadowmoon called it at one time.
"Shadowmoon Ruins" were likely intended to be the ruins of Fortress Shadowmoon or the Shadowmoon Clan's settlement holdings which were originally south of Hellfire Peninsula according to Warcraft II's maps (listed as "Shadowmoon Lands" or "Shadowmoon Clan"). In the earlier maps, "Shadowmoon Lands", the Shadowmoon Clan's held territory, the eponymous Shadowmoon Valley, was located in the southern regions of the continent south of Hellfire Peninsula. It was likely possible that the ruins were intended to be the ruins of the Fortress Shadowmoon which were reduced to ruins according to the Warcraft II expansion pack's story.
In the Shadows & Light, 2004, the "Black Citadel" is referenced, and its its location is implied to be on the Hellfire Peninsula. Outland and the description of fortress is clearly described how it was in The Frozen Throne campaign.
"Illidan the Betrayer stands as the lord of Outland and rules his domain from a massive, black iron ziggurat. Ner'zhul was originally responsible for this hulking edifice, but now blood elves, naga, and Illidan's few other allies roam its corridors. The naga live in underground sewers, and the upper levels teem with blood elves, traps, evil and death. Rumors tell that beneath the citadel sprawls a great prison, trapped within are heroes from previous wars, languishing in unknown solitude."
In World of Warcraft The Roleplaying Game, 2005, it discusses the Black Citadel, but does not mention its exact location;
Illidan the Betrayer stands as the nominal head of Outland, ruling from a fortress called the Black Citadel.
However Rise of the Horde, 2006, claims that the Draenei Temple of Karabor was clearly renamed the Black Temple, after being called Karabor. Which implies that it never changed names since then.
In Monster Guide, 2007, it is confirmed that the building Illidan's forces attacked and took from Magtheridon was known as the Black Citadel. Although its unknown what structure in which location its in reference to.
"This group of blood elves then helped defeat Magtheridon and claimed his Black Citadel as their own."
To make matters even more confusing, the official World of Warcraft Underdevelopment page, claims that the Black Temple was the;
"...prime staging ground for the Burning Legion's campaign of destruction..."
The prime staging ground for the Burning Legion from Outland in The Frozen Throne had clearly been established to be located in the Black Citadel during The Frozen Throne.
In TBC, "Behind the Scenes" DVD, one of the designers states that players had only visited Hellfire Peninsula during Warcraft III, implying that Black Citadel was on Hellfire Peninsula.
However, according to Blizzard, confirms that Magtheridon ruled from the "Black Temple" during events of Warcraft III, and that he was moved to Hellfire Citadel after his defeat by Illidan. This further confirms that Black Temple and Black Citadel are the same structure.
The Temple of Karabor had once been sacred to the draenei, before orc warlocks claimed the massive structure as their own and renamed it the Black Temple. After the Legion came to Outland, however, it was Magtheridon who ruled from the brooding fortress. He controlled all but small pockets of Outland and continuously reinforced his army by summoning further demons through the portals.
While Magtheridon had crushed many powerful foes, it had been ages since he had been challenged by one who could rival his own might. Thus was the pit lord taken largely by surprise when Illidan and his allies broke through Magtheridon's army and laid siege to the Black Temple. Soon after, Illidan crushed Magtheridon's defenses and cast the Legion's general down.
In the Black Temple trailer, It discusses how the Draenei Sanctuary first belonged to the draenei, then Magtheridon, then Illidan.
While there is a confirmation that Black Temple and Black Citadel are one and the same, it still leaves the mystery of why the structure was moved from Hellfire Peninsula down to Shadowmoon Valley.
It should be noted that the four structures often argued as being part of the history of the Black Temple do not always match up when comparing the architectural styles used in each of the games. It adds further confusion to which structure is which, and even if they are connected at all.
In The Burning Crusade it looks more like Horde fortress of Warcraft III, with some similarities to horde barracks in Warcraft II.
A series of about three black iron and stone ziggurats built above ground. Aqueducts, sewers, black columns, stone arches, and statues were all found underneath the ground.
Fortress ShadowmoonFortress Shadowmoon was a traditional Warcraft II style horde fortress. It is described in the game's story as having towering spires like obsidian blades reaching into the skies. May be related to the Shadowmoon Ruins in Warcraft III.
Black TempleA series of steps leading to a series of walls, and platforms surrounding a ziggurat/pyramid. It shares a distinctly draenei aesthetic style, although it has darkened since it was first built.
Before Blizzard's confirmation that Black Temple and Magtheridon's Citadel were one and the same, a few prevailing assumptions existed by various fans.
In another camp of fans, Black Citadel and Black Temple were seen to be the same structure, with the Hellfire Citadel seen as a separate structure.
Additionally, some believe Fortress Shadowmoon somehow survived its destruction as recorded in Warcraft II, and is the same fortress as the Black Temple, mentioned in the Underdev page - which is still possible, since the Black Temple stands exactly at the place of Shadowmoon Forteress, which was the headquarter of the Death Knights, former pupils of Gul'dan.
While there are some fans that believe the Shadowmoon Ruins in Warcraft III maybe a reference to the ruins of the Shadowmoon Fortress, or at least ruins representing ruins in Shadowmoon Valley.