Wanted to provide some more info for those curious about this. Note that I mostly read European news outlets and don't have any medical background, but I tried finding articles from various sources to the best of my ability.
Pfizer, Moderna and JNJ did not make it a priority to provide larger percentage of production to non-US markets.
There have been some countries trying to shame US country/pharma companies into selling (at reasonable/cheap cost) the vaccine.
I think that once vaccine is available in quantity, the rollout will go well in Canada.
(I can imagine that if/when the US-Canada border re-opens, there might be a run across the border to get a shot.)
The vaccine produced by Pfizer was created by the German biotech company BioNTech, which decided that Pfizer had the best parameters for quick mass production.
The technology used, mRNA, is the same the Moderna (their key founder was a Maple Leafs fan) is based on. There's a
long but very well written article that goes into the background of both companies and also credits Kariko, the Hungarian scientist that made the crucial discoveries despite many years of rejection for grants together with Weissman, immunologist at U Penn.
Anyway, countries directly negotiated deals with the pharma companies with the supply chain and production lines able to produce these vaccines, and the supply and these contracts ultimately lead to how vaccines are now being distributed. Those with less favorable deals (for 'first-world' countries, it is mostly about getting early access then just cost) have been trying to influence the process as some of the production lines in the supply chain may be in their country, leading to geo-political meddling.
Recent research paper published on the geo politics available here.
I found
this article to have some good coverage on the challenges of producing them at scale.
Lipid production is among them, and
Canadian company Acuitas Therapeutics is in the Pfizer supply chain.