Like the previous high-definition port in the Zelda series (The Legend of Zelda: The Wind Waker HD (2013)), this HD remake was released during the 10-year anniversary of its original, The Legend of Zelda: Twilight Princess (2006).
This is the only Legend of Zelda game in the series to be officially developed for and released separately on three different Nintendo systems (not counting emulated versions of games via Virtual Console). The original versions for the GameCube and Wii were developed and released almost simultaneously in 2006, and the HD remake was released for the Wii U in 2016. While it is true that The Legend of Zelda: Ocarina of Time (1998) was initially released on the co1077717, and subsequently developed as The Legend of Zelda: Ocarina of Time Master Quest (2002) version for the GameCube and The Legend of Zelda: Ocarina of Time 3D (2011) for the co0914333, the GameCube version was always part of a collection or included as bonus content, and never sold separately.
The Hero's Shade (the skeletal warrior who teaches Link sword techniques throughout the game) is the Hero of Time from Ocarina of Time and Majora's Mask, who died lamenting he wasn't remembered as a hero, as well as not passing on his skills.
Contrary to the original The Legend of Zelda: Twilight Princess (2006) and The Legend of Zelda: Skyward Sword (2011), this game continues the long series tradition where Link is left-handed. The former games were initially released for the Nintendo Wii console, where Link's sword was controlled by the Wiimote that was typically held in the right hand. So as to not confuse players, Link was made right-handed in those games. In the Wii version of Twilight Princess, everything was mirrored as compared to the GameCube version (i.e. East in the GameCube version was West in the Wii version), so this HD remake is identical to the GameCube version with regards to the world orientation.
According to the official Legend of Zelda timeline that was created by the makers themselves, the Zelda chronology is split in parallel timelines during The Legend of Zelda: Ocarina of Time (1998). This created a Child Era and an Adult Era timeline. The Legend of Zelda: Twilight Princess (HD) is a sequel to the Child Era of Ocarina of Time, and to The Legend of Zelda: Majora's Mask (2000)..