Were the War of 1812 between Britain and America and the War of 1812 between Napoleon and Russia at all related? They were not only fought in the same year but also over the same general reason, trade between nations when Napoleon wanted to monopolize world trade. But were the two wars ACTUALLY related in any way?
Yes, the two wars were indeed related, and even rather closely. Both wars were tied to Napoleon's ongoing war with Britain.
Napoleon had set up the Continental system to boycott British trade; this led to the invasion of Russia, while Britain's impressment of American sailors led to the War of 1812 with the United States of America.
Having earlier failed to defeat England on the high seas, Napoleon decided to bring England to its knees by destroying its trade. In 1806, he established the "Continental System", which forbade the importation of British goods into any European country that was under French influence.
The trade war that ensued between England and France, combined with the trickery of Napoleon, drew the United States into the War of 1812 with England.
Russia's opposition to and eventual secession from the Continental System led to Napoleon's invasion in 1812.
The War of 1812 between Britain and America was very directly related to the Napoleonic Wars in Europe (which included the French invasion of Russia).
The War of 1812 was a by-product of the Napoleonic War of 1803 to 1814. It's origins lay in the increasingly oppressive measures adopted by France and Britain to undermine the economies of their rivals, and the problems these created for the largest, and most dynamic, neutral maritime trading nation. The fractured state of American domestic politics also played a part in forming the crisis, and greatly affected the conduct of the war.
Source: The Naval War of 1812, Ed. R. Gardiner (Caxton, 1998)
Without the Napoleonic Wars, the War of 1812 would, almost certainly, have never happened. American sea trade would not have been interferred with and the British would not have needed the large number of sailors that required impressment, which in turn provided one of the triggers for the war.
Of course the US would never have invaded Canada if the leadership didn't think that the US could win. They thought it could win because Britain was already in a mortal battle.
The British commitment of forces to the war was quite minor for that same reason.
Once Napoleon had been defeated, the British committed more forces and successfully raided Washington and unsuccessfully raided New Orleans.
The Americans and the British both won the war but the Native Americans (British allies) lost badly. There was considerable suffering among Upper Canadians due to scorched earth tactics of the Americans.