In Scotland, Elizabeth I is the ruler known south of the Border as Elizabeth II. Officially, she is Elizabeth Regina, since one is rarely the First until there is a Second to follow. Letterboxes in Scotland, plaques left like spoor after Royal openings, and official documents all refer to Elizabeth Windsor as ER rather than EIIR
The Union of the Crowns that made the ruler of England also the ruler of Scotland occurred under James VI of Scotland, usually referred to as James I of England. He was successor to Elizabeth Tudor, who never reigned in Scotland.
This messy numbering problem crops up from time to time. The oath of loyalty sworn by new Members of Parliament is phrased differently for Scottish MPs than for English and Welsh ones. There is conflict now because the naturalisation oath being proposed in Parliament refers to the English queen.
This is all a legal nicety. But after centuries of bad blood between England and Scotland, we should be grateful it's only a squabble about numbers.