Both rent and home prices are driven by supply and demand, that is, what the market can bear.

In both cases supply is the same, but for ownership, the market is global. You can live on the moon and own property in Vancouver. The price of Vancouver property is constrained only by the limits of how much foreign capital is available to be safely parked in Canadian real estate, not by the population of Vancouver. As you can imagine there is considered more of the former than the latter.

However, the market for rentals is constrained by the number and salaries of people who actually live in Vancouver. Nobody rents an apartment in a city in which they don't actually reside. You can't charge $3,000/month for an apartment in Vancouver because no one will be able to afford it. In Vancouver a junior engineer earns $60,000/year.

Vancouver salaries aren't higher than anywhere else in Canada (in fact they're lower than Calgary and Toronto, both of which have cheaper housing, and about on par with Montreal which has MUCH cheaper housing), so despite the crazy property market this keeps rents down.

SF's crazy rents are driven by the tech industry salaries that are much higher than anywhere else in the country (or in the world for that matter).

SF prices are driven by intense demand due to the tech industry. Tech continues to import more and more people but there isn't enough room for everyone.

Vancouver prices are driven by speculation, primarily from international investors. The actual demand for housing in the city is comparatively low, and the typical salary for white collar work in Vancouver also doesn't support sky-high prices.

The large disconnect between sale and rent prices represents the large disconnect between who is buying vs. who is actually living in these homes.