To make a difference means to have a significant effect (or no effect) on a person or situation. I believe that it is incorrect to say it makes the difference in this context. It is more appropriate to say it "makes all the difference", which means that it not only made a difference, it made more of a difference than anything else. That is really what they mean when they say "makes the difference".

This simply means that the outcome is changed or will be changed by "it". This usually indicates a positive change, rather than a negative one, but that can also depend on the specific change that is made. When using "a", the effect on the outcome is usually small or ambiguous. When using "the", the change is usually something known or the outcome is decided by the change. For example, you might say "He gave $10 to a homeless man. There are thousands of homeless people, but it makes a difference to that man." This is a small change. The man is still homeless, but perhaps he can buy some food. "I want to buy a house, but I need a bank loan. It makes the difference." This means that if the speaker does not get a loan from a bank, he will not buy a house. The outcome is decided by the change of having a loan.

Hamzeh, it's as simple as that:)

To my mind, when you know exactly what is the difference you should use "the" before the difference and inversely while u don't know, you must use "a" before it.