Please help me clarify my own knowledge. I was taught in my middle school geography class that “United Kingdom” is the proper name for the union of England, Scotland, Wales, and N. Ireland, “Great Britain” is the proper term for the island on which England, Scotland and Wales are located, and “Britain” is generally not really a proper term, but is generally used to synonymously with “United Kingdom”. Do I have this straight?
Yes, spot on.
The shorthand of GB/UK to mean England sadly has taken root over the last 300 yrs and to many people outside our island, UK and GB are just other words for England. Which, as you said, is wrong.
Ironically, the phrase Great Britain was coined by a Scot, James I, a Scottish king who joined the English-Scots thrones, and the British Empire was coined by Dr John Dee, the famous Welshman of the 17th C.