In that original sense “a difference” means “a distinction”. We have to know what we can eat and what we can’t, and to have the moral strength to accept only what is permitted and to reject other things however attractive.
In modern English, there is a secondary meaning to making a difference: living in such a way that our deeds make our society better and finer, leaving behind a world that is different, however much or little, because we were there.
It doesn’t necessarily mean that the whole of history is changed because of us, but that we help mankind to edge closer to its goal.
One way of defining that goal is to make the world a Gan Eden without the sorrow and suffering that human beings cause one another. We will get there eventually.
Where Gilbert and Sullivan say, “My object all sublime I shall achieve in time”, we prefer to say, “we – all of us together – shall achieve in time”… provided we all make a difference.