The answer to your question to complicated - complicated not the least by the fact that people cannot agree with the assumption behind your question. I introduce my recent book, The Folklore of Cornwall: The Oral Tradition of a Celtic People with the following paragraph:

The folklore of Cornwall is often overlooked when compared to collections from elsewhere in Europe, and yet Cornish volumes of legends and folktales represent some of the first to appear in Britain. These publications preserve outstanding expressions of belief and story. Neglect of this material has been in part because it is typically lumped together with the traditions of English-speaking Britain. Indeed, the question of whether Cornwall should be regarded as just another English county or as separate from England is at the heart of why the consideration of its folklore is often diminished: it is the position here that Cornish folklore is distinct from traditions gathered in what can be called ‘England’ or ‘the rest of England’ depending on one’s point of view.

For the full introduction, see this link.

Most Cornish enthusiasts do not regard Cornwall as "simply a county of England [that] ... is not really seen as a separate entity" - to borrow your words. The Cornish are quick to point out that it had its own royally recognized ruling government - the Stanary Parliament - which was autonomous from the Parliament in London and that the Act of Union (1707) failed to integrate Cornwall the way that the law addressed Wales and Scotland. These enthusiasts argue, therefore, that Cornwall should be treated as a separate Duchy, ruled by the crown in the fashion of the Isle of Man or the Channel Islands, but not as a county of England.

Of course, perception is everything, and most English do not share in this view of Cornwall. Indeed, with many wealthy people from outside Cornwall owning second homes in Cornwall, there is a threat to the indigenous culture, dialect (of English), and sense of autonomy.

At the same time, there is a revival of the Cornish language with some 500 speakers, and although the language was repeatedly declared dead, it seemed to have consistently had people who understood it: documentation of the "last speaker of Cornish" often includes the observation that few people could understand what the person said before her (or his) death.

Cornwall survived as an autonomous entity for as long as it did largely because it is at the end of a remote peninsula. Even Devon is cut off from England proper by the historical "pinch" caused by the Somerset marsh at the north, but Cornwall itself is nearly an island with its border almost entirely defined by the Tamar River. Only a small land bridge exists in the north. Other Celtic lands such as Cumbria in what is now northwest England were easily washed over by England, but Cornwall resisted because it was so far away from everything and because historically it could stand resolutely behind remote Devon and then from Devon because of the Tamar River.

My book, together with research behind an article currently in review, demonstrates that culturally the Cornish have stood apart from England. At the same time, we cannot ignore the fact that English (even if it is with a distinct local dialect) has been the language of Cornwall by any practical way to consider it for more than a century. In addition, we cannot ignore the fact that the parliament in London moves forward with its governance without making a distinction between how it treats Devon, for example, and Cornwall. In practicality, it has been, integrated into England in most ways, no matter how distinct it has remained.

So why is this the case when Wales retained its own separate identity? The answer is, really, size: Wales is larger and it has a larger population. At the same time, it was sufficiently remote to retain the Welsh language, and it was able to defend itself against English efforts to integrate that land into England.

Two sources that deal with this are

Philip Payton, Cornwall: A History. Fowey: Cornwall Editions, 2004

And the recent, excellent book by Craig Wetherell, The Promontory People: An Early History of the Cornish. London: Francis Boutle, 2018.