The Commonwealth of Former British Colonies is an organization dedicated to the Republic of Canada and Union of South Africa, in relation to the UK, that shows the common roots of the nations.
With the Republic of Canada becoming independent after WW1 and The Union of South Africa becoming independent after the Final Boer War (1921-1924), The UK had to try and keep a hold of it's remaining empire. Australia and New Zealand were given more self-control (although still Dominions) and more places were becoming more rebellious. The UK decided that for it's empire to survive it needed the former Empire's nations to join a supportive organization; The Commonwealth of Former British Colonies was established in late 1925, uniting The UK, Canada and South Africa under one head of state (although the monarchs have no control over these other 2 nations) and keeping these places somewhat supportive of the Empire. The Commonwealth is why Canada joined WW2.
World War 2 & Second Interwar Period
Canada joined World War 2 independently via the Commonwealth, but South Africa refused. South Africa wanted to show it's independence by not getting involved in the war. During the Zulu crisis South Africa sent in peacekeeping troops to stop the British and Canadians from fighting the Zulus. These two other nations banned South Africa from the Commonwealth, but this only made South Africa more determined. South Africa would never rejoin the Commonwealth, even when offered after the crisis. The British and Canadians would slowly divide in culture over the years, Canada became far more influenced by The USA then Britain.
World War 3
Both Empire and Commonwealth would serve in WW3, with the nations being predominantly supportive of the war. The USA also told Canada to join and this made sure Canada would join the war, however Canada would lose over 1,000,000 men and the Empire would lose nearly double that.
The Commonwealth continues to exert it's influence across the world and the Empire. The US is partly supportive of the Commonwealth and assists the Commonwealth when needed.
Differences between the Empire and the Commonwealth
The differences between the Empire and Commonwealth are numerous, Canada is a fully sovereign state while the Dominions and Colonies are either partly or not sovereign. Both of these entities work together, however.