I think that the term "Celtic" is often misleading. "Gaelic" music on the other hand is much more defined. Since you live in Canada you are no doubt familiar with the traditional music of Cape Breton Island. While this is broadly defined as "Celtic" it can be much more accurately defined as Gaelic, and Scottish Gaelic at that. However, this playing style has largely been lost in Scotland, and replaced with more "English" styles.