I see that Canada became independent in 1867. But someone told me it wasn't truly independent until the 1980s. Is that true? In what sense is it true? I don't see anything about it in that article or in the See Also section.
There have been several stages in the history of Canadian independence.
The Statute of Westminster, passed by the UK Parliament in 1931, acknowledged Canada as co-equal with the United Kingdom within the British Commonwealth.
Canada obtained full autonomy when the UK Parliament passed the Canada Act 1982 in 1982. This granted full sovereignty to Canada, and so marks the date at which Canada became truly independent.
As a side note, and as noted in the comments below, the Queen's role as monarch of Canada is entirely separate from her role as the British monarch. She is Queen of the United Kingdom, and also, Queen of Canada by an act of the Canadian Parliament (The Royal Style and Titles Act).
The fact that the Queen is head of state of both the UK and Canada (and also in 15 other Commonwealth nations) does not affect Canada's sovereignty as an independent country at all.
The subject isn't nearly as simple as it is for the USA. The event in the 1980s was Patriation of the Canadian constitution, which removed the power of the UK parliament to amend the Canadian constitution with the consent of the Canadian government. This was done by the UK parliament, at the request of the Canadian parliament.
That power had been retained by the UK parliament after the Statute of Westminster in 1931, because of disagreements between the Canadian provinces and their federal government about how to amend the constitution. The Statute of Westminster had made the Dominions (Canada, Australia, New Zealand, Newfoundland and South Africa, Ireland was a special case) the legislative equals of the UK, which made them fully independent states. The Canadian constitutional oddity allowed the rest of the Statute to go forward, and was eventually sorted out.