Why thank you. I wear the title with pride.
As far as the definition of "nation", to be honest all three words are rather vague, and this one especially. It's really a word describing a level of family: you have your immediate family of mom and dad and siblings, your extended family of cousins and aunts and uncles, your tribe or clan of distant relatives, and your nation consisting of several related tribes all sprung from one ancestor. How far back that ancestor is varies from case to case, and there's really no hard and fast rule for determining it.
The issue is further clouded by the notion of adoption. Just as a kid can be adopted into your immediate family, an immigrant can be adopted into your nation. This is what happened with the US and Canada. Early Americans would have considered themselves an offshoot nation from the English nation, having common ancestry and culture. As immigrants swelled into the country, they were (eventually) adopted into the nation, which is why Americans tend to refer to themselves as a single nation (interestingly enough, the different tribes of Native Americans refer to themselves as "nations" as well, distinct from the larger American nation).
As for the Scots and Welsh, the Scots were actually quite distinct from the Welsh. Scotland was, at the time of the Roman withdrawl, populated mainly by Picts and Celtic Bretons (of the same people as the Welsh). However, the Scotts (or Scotti) themselves were actually invaders from Ireland who established a kingdom for themselves in what is now known as Scotland. The disparate groups eventually intermingled and became a distinct nation from the Bretons who became known as the Welsh.
All in all, the rules for distinguishing one nation from another are extremely vague. It's one of those things that are hard to define exactly, and yet people are still able to identify it when they see it -- like "patriotism" or "pornography". Theoretically it is, as I said above, the descendants of a common ancestor, but in practice it tends to be a little more complex than that.
Crap, now I'm late for work. Bah.