Why was Frederick I only called "King of Denmark" while Christian III was named "King of Denmark and Norway"?
Election of Christian III The election of Christian III as king of Denmark and Norway on 4 July 1534 was a landmark event for all of Denmark and Norway. It took place in the church in the town of Rye, eastern Jutland, where the Jutlandic nobility elected Prince Christian, son of King Frederick I and Duke of Schleswig and Holsten, as king. This brought about the Count's Feud ("Grevens Fejde") and later also led to the implementation of the Protestant Reformation in Denmark and Norway.
Competitors for the Crown of Scotland With the death of King Alexander III in 1286, the crown of Scotland passed to his only surviving descendant, his three-year-old granddaughter Margaret. In 1290, the Guardians of Scotland, who had been appointed to govern the realm during the young Queen's minority, drew up the Treaty of Birgham, a marriage contract between Margaret and the five-year-old Edward of Caernarvon, heir apparent to the English throne. The treaty, amongst other points, contained the provision that although the issue of this marriage would inherit the crowns of both England and Scotland, the latter kingdom should be "separate, apart and free in itself without subjection to the English Kingdom". The intent, clearly, was to keep Scotland as an independent entity.