Theory: Donkey Kong Island Remains the Same Island

Arguments

Argument 1: The island is called Donkey Kong Island in DKC and DKCR.
It is very rare in the Mario World, that two different locations have the same name.

Argument 2: In DKC, DKI has a large forested area called Vine Valley. In DKCR the forest area features a level called Vine Valley.

Argument 3: Following Argument 2 Vine Valley from DKC and Vine Valley from DKCR are the same place. Comparing the DKI’s appereance in DKC and DKCR with Vine Valley positioned, many similarities in the islands layout can be found:
- The Cave area from DKCR (a cave system with lots of mines) is in the same place as the Monkey Mines from DKC.
- The Ruin area from DKCR (a dense and large jungle, where you can find many Kong related ruined temples) is in the same place as the Kongo Jungle from DKC
- The Factory Area from DKCR is in the same place as Kremkroc Industries Inc. from DKC
- In level 7-1 and 7-3 from DKCR a large lake is seen in the background. Kremkroc Industries Inc. Also has a prominent lake between the factory sites called Poison Pond.
- From the Kremkroc Industries Inc. overworld map you can spot a large mountain in the background. A similar shaped mountain is visible from the Cliff levels 6-6, 6-8 and 6-B from DKCR.

These levels are right in place to be seen from the Factory, hence Kremkroc Industries Inc.

Argument 4: In the Factory level 7-R from DKCR some oil derricks can be spotted in the background. Kremkroc Industries Inc. from DKC features a level called Oil Drum Alley. The oil from these derricks might be refined in the close Oil Drum Alley.

Argument 5: The Beach area would be right in place where the Kong face used to be.
The Beach is one of the few areas not to feature ruins, unlike the neighbouring Jungle and Ruins, probably because it was covered by the Kong face before.

Argument 6: In the Chimp Caverns from DKC, which laid underneath the Gorilla Glacier, the ground cracks open due to volcanic activity, foreshadowing the soon erupting Volcano that potentially destroyed the mountaintop with Gorilla Glacier on. Where the Gorilla Glacier used to be in DKC a large active volcano is in DKCR.

Argument 7: DKI in DKC is described to have so many caves it‘s like a Swiss Cheese, making it very likely the carved Kong face was destroyed during an earthquake like event, potentially the volcano eruption.