There are times when the three words mean the same thing, but not always. An advantage can mean a superior position in relation to someone or something. I have an advantage over my competititon because I have access to cheaper materials. Benefit and profit are neutral in this regard - they do not necessarily imply superiority in any regard. Profit can also mean the difference between what a business or enterprise takes in and what it spends. If I receive 20 dollars for an item that I spent 15 dollars for, I have made a profit of 5 dollars. Benefit and advantage would not be used in this way.

Maybe this will help: Imagine a situation between you and another person. You are equals. ADVANTAGE: If the situation changes so that you have an advantage, you are now greater in some way than the other person, so you are no longer perceived as equals. BENEFIT: In this situation one person can give or do something that benefits the other person but both people are still generally perceived as equals. PROFIT: This word is usually applied to money but can be applied to people. If you profit from a situation, then it costs the other person something. This can change the perceived status between people. Please keep in mind that my definitions are very GENERAL in nature. I am only trying to help you see the difference. Each of these words can be used, and are used, to mean the same thing or nearly the same thing. Hope this helps!