Scotland is a "country", but "country" is a vague term. Scotland is not a sovereign state, which is what most people think of when they think of countries. In fact, other than the weirdness that is the UK, I can't think of any place that has "countries" that are not also sovereign states.

There are some places like Catalonia, or the Basque area that want to be / claim to be countries, but that's more about sovereign status. They wouldn't be satisfied being recognized as "countries" while still under the rule of Spain / France.

The only time this weirdness really shows up is at the World Cup, where the 3 separate countries within the UK each try to send a team. Meanwhile at the olympics they compete as one under the Team GB banner (which is its own weirdness because normally Great Britain excludes Northern Ireland, which is only included when you talk about the United Kingdom. But, Team GB includes Northern Ireland. In yet another exception, sometimes athletes from Northern Ireland compete as part of Ireland in some sports, not as part of the UK / Team GB.