Clicking on a champ is the same thing as near it? Or not...

Clicked on a box, started attack animation and then lost it because the minion was untargetable. A different time, the minion became targetable and my auto was instant to it due to auto attack preference. Third time minion became targetable but clicked on it and did not auto attack. Just sat there waiting for command preventing the kill and it then died on its own. I don't understand the concept of clicking near, vs clicking on. Sometimes the game mixes the two up and you get an unintended outcome.