It was similar, it was “wild” and in many ways it was spawned by the expansion of the American West and associated land claims.
You can divide the old Canadian West into two components:
Rupert’s Land which the Hudson’s Bay Company administered. This area includes all of the river basins that flow into the Hudson’s Bay. As the majority of these rivers were north of the 49th parallel and east of the great divide in the Rocky Mountains, this became a rough dividing line between American and British territory in the west.
The Columbia District which was also administered by the Hudson’s Bay Company, but who was co-occupied by American fur trading companies. This area included the entire Columbia river basin in what is now British Columbia, Washington, Oregon and some parts of what is now Montana and Idaho. In 1846, The Oregon Treaty extended the 49th parallel to the Pacific Ocean creating the Oregon Territory and British Columbia.
The areas the HBC laid claim to were lawless and harsh. Up until the 1870s, however, the colonial authorities had no agenda to displace natives to pave the way for European economic interests in the same way that “manifest destiny” did in the US. This all changed after confederation in 1867, and pressure in London and Ottawa to amalgamate the British North American colonies. In 1870 the new Dominion of Canada bought Rupert’s Land from the HBC, and in 1871 British Columbia joined confederation after successfully negotiating a trans continental railroad to carry BC commodities to the east coast. This immediately encouraged Ottawa to negotiate treaties with the aboriginal peoples of the Canadian plains, in order to secure land for a new railroad and large scale agricultural settlement.
This, in many ways, was far more orderly than America’s expansion west. In Canada, this was all negotiated and almost peacefully attained. So the settlement itself wasn’t as sporadic or violent. However....
During this time period the Canadian plains had a lucrative whisky trade. This was mostly ran by American whisky traders who took advantage of the lawless “whoop up country” north of the 49th parallel. American and newly arrived European ranchers also started migrating to the northwestern plains. The Whoop Up Country was extremely lawless. Murders were commonplace. Gambling and prostitution were common. After a particularly horrifying massacre in 1873, the Canadian government sent a paramilitary force called the Northwest Mounted Police to suppress the illegal trade. So effective was this force it gained a Royal title, and the newly created Royal Canadian Mounted Police became a renowned symbol of Canada thereafter.
There was also a rebellion in the 1880s when the Metis people (a unique cultural group spawned by the interaction of European fur traders and aboriginal Women) became disenfranchised from Ottawa’s push west. This culminated into a military conflict know as the Northwest rebellion.
Otherwise the Canadian west had all of the commonalities of commodity based communities in a mostly lawless and sparsely populated area: red light districts, gambling halls, shoot outs, and high rates of alcoholism. There were cowboys on the Canadian prairies, religious refugees from the US and Europe (including Mormons and Hutterites), black cattle workers escaping discrimination And seeking opportunity (most notably John Ware), and folks from around the world who just wanted a new chance in life. Around 1 million Americans migrated to the Canadian plains from the 1880s to 1910s, however this number was offset my massive migrations of French Canadians to New England during the same era.
So TL:DR: The Canadian west was every bit as “wild” as the American West, but was settled in a rather different manner due to its affiliation with the British Empire.