There is no such thing.
Let's take a popular, though simplistic, situation where we use the phrase lead by example frequently: An underage party where there is alcohol present. Let us identify someone at the party we want to lead - for this scenario let's choose two students, one male, one female. Both are very popular, intelligent, hard working, and admired throughout the group present.
The male decides he is going to lead by example and not drink. He stands prominently in the center of the party, where all can see him, clearly not drinking. When offered a drink, he states loudly "No! I am not drinking. This is wrong". He even gives disapproving looks when others walk by with alcohol.
Now let's see what our female leader does.
After watching her peer, she decides that she will set the example, AND lead. She goes to the center of the room, clearly not drinking, she calls for the attention of the party, and explains to the group that she is not drinking because she thinks it is wrong, and tells the group they should not drink either. She provides the crowd a clear argument. She tells the group they should throw out the drinks and get some soda.
So what is the big difference between the two?
Simple, he did not lead, he only set the example. To lead is an action. To lead there must be a declarative like "Follow me", "Do what I do", "Do this" or "Don't do that", otherwise you are leaving it up to your followers to determine who's example they should follow. Our male leader in this scenario may have set the right example, but his actions were not necessarily enough to inspire the actions of others - probably because no one even knew they were supposed to look to him to lead. Despite his popularity and capability to lead, no one knew they were supposed to follow him, because reputation and status, don't automatically imply leadership. There must be a call to action. What was the difference? Our female leader put herself out there with the declaration. She bravely stood out from the crowd - not just with her actions, but by declaring herself a situational leader and giving guidance on what she wanted to happen.
You see, when you just "lead by example" no one knows they are supposed to follow you. They don't know your vision. They don't get any guidance. They don't even know you are the one they are to be looking to for leadership.
And therein lies the problem with "lead by example" in America today. We can all say that the above situation is silly and sophomoric, but is it that far away from some of the issues we deal with today? Would we want people at a party where a woman is being harassed to "lead by example"? No, we would want them to lead and say "Stop", physically stopping them if needed.
We spend a lot of time leading by example in the country right now - in other words "taking care of our own stuff". Because leading by example is just making sure you are doing the right thing, it doesn't effect anyone else. In fact, it is even kind of arrogant to think that people would just look at you and think "Wow, that person is doing this - I should do that too".
Look, I am not taking away from the idea of setting the example - it is great to do the right thing - and more people should do it - but it is not leading. Leading takes action. So what you should want to do is set the example, and lead.
J.C. Glick, LTC, U.S. Army (Ret.), Director, Leadership Resiliency with 360 DEVELOPMENT™ part of Destination Athlete®