"Certainly" and "Of course": what is the difference?

Is there any difference in expressing consent and assurance using adverbs "certainly" or "of course"? What would be more appropriate one in everyday conversation?

When it comes to expressing consent and assurance, I'd say the difference certainly isn't very big. :-) When faced with a question like

Can I have some more coffee?

..."Of course" would probably be a more typical reply. But there's nothing wrong with "Certainly" either (although it might sound a little more formal).

Oh, as you mention the context is everyday conversation, you should also consider something like:

Yeah, sure!

:-)

Certainly is used for emphasizing that something is definitely true or will definitely happen:

I certainly hope you’re right.
There certainly wasn’t any point in doing it now.

In this fashion, certainly is slightly different from of course.

When used for expressing agreement or giving permission in daily conversations, certainly and of course have the same meaning:

-We’d like you to explain your proposal to us in greater detail.
-Certainly. / Of course.