You'll see and hear the terms Cape Breton Island and Cape Breton used interchangably to refer to the island. The island is, of course, named after the barren, wind-swept headland, "Cape Breton", though not many Cape Bretoners seem to know this and few could tell you where the eponymous cape is. Most have never been there.
For most Cape Bretoners the island is simply "Cape Breton".