The timeline is a bit screwy in the old zones. I'll paraphrase.
Thrall makes Horde (Warcraft 3)
Thrall rules Horde (Vanilla)
Thrall meets Garrosh, son of Grom Hellscream, on Outland. Takes him under his wing. (Burning Crusade)
Thrall is apprehensive about invading Northrend. Garrosh disagrees and challenges Thrall. Garrosh is the victor, the Horde goes to Northrend. (Wrath of the Lich King)
Garrosh is hailed as a war hero after the events in Northrend.
Thrall renounces his title as Warchief after the Cataclysm. He passes the title to Garrosh.
Garrosh proves to be a... temperamental leader. This a quite the understatement. (Cataclysm, Mists of Pandaria)
Garrosh is besieged in Orgrimmar. Both the Horde and Alliance eventually bring him and his forces down. Thrall attempts to execute him, but is stopped by Varian Wrynn and Taran Zhu. Garrosh is to stand trial for his crimes.
Vol'Jin is named Warchief.
Garrosh escapes his war trial with the help of two dragons and a time machine.
Garrosh uses said time machine to create an alternate timeline where the Orcs of Draenor never knelt to the Burning Legion.