England & Northern Ireland: Different National Anthems (Same Tune, Different Words)

They do not sing the same national anthem.

England

• Anthem: "God Save the King" (currently; "Queen" when monarch is female).
• Status: De facto national anthem of the UK; used for England at most sporting events (except Commonwealth Games where "Jerusalem" or "Land of Hope and Glory" sometimes used).

Northern Ireland

• Official Anthem: "God Save the King" (as part of UK).
• Sporting Context (Majority): At international sports (football, rugby, Commonwealth Games), the NI team uses "Londonderry Air" (tune of "Danny Boy") as its team anthem—distinct from the UK/England anthem.
• Political Sensitivities: Unionists prefer "God Save the King"; Nationalists/Republicans reject it. "Londonderry Air" is a compromise neutral tune.

The Core Confusion

Both can use "God Save the King" (same tune, same words currently). But Northern Ireland often uses a different anthem for identity representation, while England uses the UK anthem by default. The premise of the question likely stems from hearing "God Save the King" played for both in some contexts (e.g., UK state events), but they are distinct in international sporting representation.