Do the terms 'Great Britain' and 'the United Kingdom' have identical meanings?

Okay, let's break down the difference between Great Britain and the United Kingdom. It's a common point of confusion! Great Britain refers to the island that comprises England, Scotland, and Wales. Think of it geographically – it's the physical island. The United Kingdom, officially the United Kingdom of Great Britain and Northern Ireland, is a political entity. It includes that same island of Great Britain, plus Northern Ireland. So, while Great Britain is a part of the United Kingdom, they aren't the same thing. The UK is a sovereign state, a country, while Great Britain is a geographical term. A helpful analogy is thinking of the UK as a company, and Great Britain as one of its major divisions. They're related, but not identical. That's why saying they have identical meanings is false.
Picture the UK as a family where Great Britain is the parent, and Northern Ireland is the child, separate but still part of the same family.