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The Super Kongs are a white-furred lookalike of Donkey Kong and Diddy Kong respectively, wearing blue clothes instead of red. They each represent Donkey Kong and Diddy during the Super Guide mode of Donkey Kong Country Returns, and have a very similar role to Super Guides in other Super Mario series installments.
Donkey Kong Country Returns / 3D
If the player loses eight lives in a level (or five in the 3DS remake's easy mode), the Tutorial Pig appears and offers to activate the Super Guide. If the player selects yes, then Super Kong appears and completes the level for him.
Any items collected by Super Kong, such as bananas, Banana Coins, or even Puzzle Pieces, are not kept by the Kongs themselves. Super Kong always goes on a predetermined path to the end goal, meaning he does not access hidden areas or any bonus room.
While Super Kong can be activated during the final boss level, Tiki Tong Terror, the end cutscene still shows the normal Kongs as opposed to the Super Kongs, who appear in most other cutscenes.
It has been mentioned that the choice for Super Kong's tie to be blue instead of red was caused by the sunset levels of the game, which have Donkey Kong in silhouette and, therefore, required Super Kong's tie, as the only thing shown in those levels, to be a different color to differentiate the two.
Super Smash Bros. Ultimate
A white-furred variant of Donkey Kong appears as a playable skin throughout the Super Smash Bros. series. The only time where this was used as an explicit reference to Super Kong was in Super Smash Bros. Ultimate, where Professor Chops's spirit battle involves fighting a white-furred Donkey Kong, alluding to the connection between Professor Chops and Super Kong in Donkey Kong Country Returns.