I think the phrase "with full intention" means quite directly that he was aiming to kill Ralph. Sometimes when people aim a weapon at another human being, the idea of killing another is just too revolting to actually bring one's full will to intentionally kill a peer human being. In this case, Jack was full of animal instinct, he had a vengeful attitude, and he had let his adrenaline get the better of him. Of course, after just having killed Piggy, Jack's rage is flowing through his own body with great force. Noting that Ralph associated himself with Piggy and there have essentially been two forces of boys against each other for a few chapters, this intentional attempt at murder makes sense.
Earler in the chapter, Roger throws a rock in between Samneric but aimed to miss. We can assume Roger's intention was to scare these little boys. Thus, the author drew a contrast between the different purposes for acting aggressively toward peers.