The Horde has historically been the main alliance of orc clans & their allies.
The Orcish Horde (AKA Old Horde): Formed by Ner’zhul/Guldan (depending on continuity) shortly before the orcs invaded Azeroth (year 0), and was disassembled after their defeat in the Second War (year 8).
Horde (Playable Faction), AKA New Horde: Formed by Thrall after he led the clans from the Eastern Kingdoms to settle on Kalimdor, and is one of the two playable factions in WoW. It includes the orcs, tauren, Darkspear trolls, undead and goblins, in addition to some allied races.
Iron Horde: Formed in alternate-timeline Draenor by Garrosh Hellscream after he escaped his trial in Azeroth.
Dark Horde: After the Orcish Horde’s defeat in the Second War, many survivors escaped to form rogue parties. A group of them served black dragon Nefarian in Blackrock Mountain.