You're used to say Holland or the Netherlands for that nordic country thinking that's two words for the same thing. Well, I'm afraid I've to tell you you're in the wrong.
Actually, Dutch people don't really care, they seem to have forsaken being mad at foreigners after all these years. But that doesn't forbid us to tell true from false.
Holland is NOT the country (well, there were a County of Holland for four centuries and a Kingdom of Holland for four years) but Netherlands are and actually, the Holland is a part of the Netherlands since it's the union of two of its twelve provinces (North and South Holland).
Amsterdam is situated in North Holland and as it is the biggest city in the country, it would be logical its capital to be Amsterdam. However, that's not the case. Haarlem, a nearby city on the West of Amsterdam, is actually the capital of the North Holland.
For your culture (and because that's way more than I wanted to share in this article), below is a really interesting video on differences between Holland and the Netherlands.trips, amsterdam