The terms Cape Breton Island and Cape Breton are used interchangeably to refer to the island, even on this website. The island is, of course, named after the barren, wind-swept headland, "Cape Breton". Not many Cape Bretoners seem to know this and only a few could tell you where the eponymous cape is. Most have never been there…
For most Cape Breton Islanders the island is simply "Cape Breton".

Map of Cape Breton Island