Black Orc
The Black Orcs are a sub-faction of the Orcs and Goblins in Warhammer Fantasy, and are quite possibly the hardest front line unit on the south side of Warriors of Chaos. Clad in what amounts to plates of kettle metal, brandishing various weapons of the beating, slashing and crunching variety and with a mean streak at least a few miles wide, Black Orcs are the classic elite unit of the Orcs and Goblins faction, and is comparable to Empire Greatswords, Tomb Guard and Temple Guard as melee-units made for krumpin' without being Blood Dragon-like expensive and killy.
Black Orcs are named after their dark green skin and their black armour, which stands in stark contrast to the usually ragtag look of other Orc units, which is mostly painted by shit and blood. This stems from the very first unit of Black Orcs, which was originally slaves to Chaos Dwarf slavers. Tired of their Orc workforce constantly beating each other up over not having enough fights, the Chaos Dwarfs tried to create the perfect slave, taking the most disciplined and tempered Orc slaves, filling them with dark magics and training them mentally and physically, as to get a worker who'd work hard for their masters. Unfortunately, the Dwarfs forgot that Orcs are Orcs, and this new sub-species banded together and carried out an elaborate escape plan which included copious amounts of dead Chaos Dwarfs. The Black Orcs broke free and joined nearby Orc tribes, but had difficulties fitting in because of their disciplined way of fighting and ability to work as a team. As such, Black Orcs are more like wandering bands of elite warriors who few Orcs particularly like for their un-Orcy ways, but won't mind when they get into a scrap and show how absolutely hardcore they actually are.
Normal Orcs consider Black Orcs as being unintelligent and weird for not wanting to scrap all the time, but on the contrary, Black Orcs have a tendency to sport a much higher ability to plan out strategies and to be able to take more stress in battle than any normal Orc, save for a Warboss. Combined with their increased size and hardy hides, and some of the best-forged Orc weaponry and armour in the entire tribe, few Orcs can match a Black Orc in battle.
On the battlefield, Black Orcs are entirely unlike the regular Orc mobs; they are highly disciplined, well armed with multiple types of weapons at hand and armoured from toe to teef. When a Black Orc unit marches, it's in almost unison, with no bickering and or grumbling going on in the regiment. Where a regular Orc is an opportunistic and barbaric berzerker, Black Orcs are disciplined, professional soldiers, executing orders to the tee(f) and dispatching their foes with both vigour and constraint.
tl:dr - Orc Space Marines made by Chaos.
Black Orcs in AoS
Black Orcs specifically do not exist in the Mortal Realms, but particularly large veteran Orcs (equal to Big Un's in Fantasy) with plate armor called 'Ardboys follow the Ironjawz around as their basic troops, attempting to emulate them and keep up by being fairly regimented and well-trained - something the surly Brutes find the be 380% Muckin' About. One can imagine they exist on their own as well as regular, armored Big Un's around the Realms.
Ruleswise, they're essentially like Chaos Warriors and Stormcasts with two Wounds and a 4+ Save and a slew of decent attacks.
40k Black Orks
Despite the fact that they are never explicitly mentioned in 40k, it is implied that they might exist, or at least will soon.
During the 11th Black Crusade, Abaddon went to a planet called Relorria. He encountered some Orks that were looting the planet, which Abaddon took as his opportunity to pull a fast one on them and do some experiments. The result of these Daemon-Ork hybrids is never explicitly mentioned, but it is apparently a success. Whether these Black Orks will end up serving the Black Legion or return to their Klans (or both) is unknown.
In terms of existing units though, the most immediate counterpart of the Black Orcs as 'the orks who do displine' are the Stormboyz who while not 'arder' then a standard ork, are more trained.