sure, of course there is certainly a difference between them! "of course" implies something is obvious. anyone can see that it must be true. "sure" just means something is true "certainly" is more strongly definite than "surely" eg: if someone asks you "do you want a coffee", and you say no, then they might ask "are you sure?", but it would be strange to hear them ask "are you certain?" - it's too strong a word here. but if the question was "i just saw someone get shot!" ; "are you certain??" i.e. the answer is very important and serious. (you can't use "of course" in this context)

sure means:1. having no doubt,such as "I'm sure he'll come" 2.certain(to hapepn,to be trusted),such as:"He is sure to come" Difference between "sure"and "certaain": 1.In British English,"certainly" and "I'm certain" are used when one really knows the truth; 2."surely" and "I'm sure"when one has only a strong hope or belief. In the sentehce"I'm not sure\certain where he is.",two words have the same meaning. But "sure" cannot be used of events: It is certain that…… 3.In British English,"certainly" is used when giving a firm "yes" or "no",and the use of "sure" or "surely" in this meaning is thought to be rather American. And about "of course",I'm sorry that I don't know the answer. Some information from dictionary.