“the crown” is an idea stemming from english constitutional law representing “the state”, i.e. the legal entity constituting the country. It doesn’t have a lot to do with the physical monarch except in metaphor. It looks like, based on some Googling, that Jamaica, which is a republic (canada is not) still uses the term “crown” in this sense: https://www.mof.gov.jm/careers/crown-counsel-mlss-legal-serv...
wanted to correct this one: I confused Barbados with Jamaica here. Barbados is a republic. I am sure its laws still use the term "the crown", but it looks like it uses the term "Public Prosecutor" instead of "Crown Prosecutor".
"English constitutional law" is any English law that pertains to something you consider to be "constitution".
The term "Crown" used to mean the prosecution in criminal cases derives from the actions of Henry I and particularly Henry II, in despatching teams of royal justices around the country, to hear cases in the provinces. Previously, such cases were heard mainly in baronial courts. In that sense, these kings made the English law more uniform, and more accessible.
One of the customary requirements of kings was that they should dispense justice. One of the classes of court in the UK is Crown Courts, which hear criminal cases in front of juries (and appeals from magistrates courts). They are not controlled by The Crown, and the judges are not appointed by The Crown.
In theory, the government here governs by the grace of The Crown; everything is by grace of The Crown. In practice, it's nonsense.
