A Chronicler and Historian are two very different job descriptions and we still have both working today, though in different forms from the past.

A chronicler primarily compiled current information into a written timeline. This information was often of local import and didn't contain analysis or research. Think of it as a book of current 'facts' as written down by the people who where alive when it happened. Some facts could be word of mouth or even fantasy, but it was basically stuff collected by people who experienced it. This timeline would be copie and sent to other places where each copy would be independently updated. This means a chronicles or annals could be the same up until a certain point and then have different facts added to them over time. The Anglo-Saxon Chronicle is a great example of a 'living' document of this nature.

Historians study the past, analyze it, compile it, synthesize it and come to conclusions based on their findings. One does not need to have lived though an event to be a historian of it.

In today's day and age you could say that newspapers, google and bloggers are the chroniclers of our time. Historians will look at that collection of 'facts' and analyze it.

A TL;dr could say that chroniclers compile the information and historians study it.