In Waterdeep: Dragon Heist, both magistrates and magisters are mentioned throughout. The lore chapter, ch. 9, "Volo's Waterdeep Enchiridion," discusses the role of magister in depth, but does not mention magistrates.
Here are some examples. I cannot cite page numbers, as I am using D&D Beyond.
Introduction: "Those charged with committing a crime are brought before a magister to be judged."
Introduction: "...for example, a successful Charisma (Persuasion) check might enable a character to bribe an official or sow enough doubt in the mind of a magistrate to have the case thrown out."
Ch. 1: "Magistrate Silmerhelve witnesses the transfer of the deed, rendering the new ownership official..."
Ch. 2: "...an evil adventurer who was exiled three years ago for attempting to bribe a city magistrate, has returned to Waterdeep illegally."
Ch. 3: "A magistrate provides the City Watch with a warrant..."
Ch. 4: "They are arrested for one or more crimes and taken to a courthouse in the Dock Ward to face sentencing by a magister."
And so forth.
Is magistrate another word for magister, or is it a separate office? Although my question stems from the 5e adventure Waterdeep: Dragon Heist, sources from any edition are acceptable.
Note: I know that the term "Magister" has another meaning in the Forgotten Realms. I am not looking for information about this type of Magister.