What are the duties of the Chancellor After asking this question,
I've realised I don't really have a good grasp on what exactly 
the Chancellor does.

I know the Vice-Chancellor runs the university, but what does the Chancellor do?

I've been told it is something like:
If the Vice-Chancellor was the Prime-minister, then the the Chancellor would be the Queen.
Though that doesn't really say all that much.

Is it also similar to the corporate analogy of: the CEO and the Chairperson of the Board of Directors?
The analogy you postulated is a good one: the commonwealth Chancellor in such systems is pretty much a figurehead and PR person for the university, if he or she so chooses. He or she may or may not also run the executive council meetings; if not, such a duty devolves to the "pro-Chancellor."