I think in the strictest sense, if you are reporting events chronologically over a period of time (not necessary defined by calendar years), then chronicles, but if you are reporting events chronologically within an annual period of time, then Annals. Events can span over years, or across a the calendar year, so the Annals would capture that as an event in yr 1, continuation in yr 2, etc whereas in Chronicles, it will be captured as a period independent (almost)of absolute time except it is chronological to the events preceding and events after. Which context can you use them in? I have not seen the words used with reference to modern record keeping - to best of my knowledge, we just use "records" (and especially with modern database, where the search function is so powerful, a chronological filing is not necessary anymore). If you are referring to historical context, then use whatever the historians used, I suppose?

They are both rather formal and old-fashioned and suggest an OFFICIAL record. In ordinary use, a simple list of events is called a "chronology." For example: 1608: Dutch eyeglass maker Hans Lippershey invents the refracting telescope. 1610: Galileo Galilei publishes his discovery of sunspots, craters on the Moon, and the moons of Jupiter. 1668: Isaac Newton builds the first reflecting telescope. A description of a series of events, as a story, using regular sentences and paragraphs, is a "history."

I would say chronological :)