Garrosh Hellscream is many things. He's brash, headstrong, arrogant, concerned for his people, determined to deliver the whole of Azeroth into their dominion no matter what anyone thinks about it, but one thing is clear. He's not Gul'dan. For all the grief I like to give Horde players (mainly because it's easy to rile Horde players up, I know, I raided as Horde for all of Cataclysm and a good chunk of Mists) It's true that on the surface, the Horde of today has changed greatly from the Horde Gul'dan created.
The Horde as it exists today is the spiritual successor of the Horde that Orgrim Doomhammer created when he seized power. Was Doomhammer a kindly, soft spoken orc who loved kittens and rainbows? No. No he was not. He was an orc who had come to power as the right hand of Blackhand the Destroyer, a hunter and a warrior who had spent his entire life in combat. He was strong, devoted to his people, and absolutely committed to an orc victory no matter the odds. In a way, minus Garrosh's bluster and bravado, the orc he most resembles from the history of the old Horde is Orgrim Doomhammer.