There's no technical difference between holding AF-ON vs. keeping the trigger button at half-press. But it's a lot more difficult to maintain half-press of the trigger button, without neither letting go nor taking a picture by mistake, compared to keep the AF-ON button fully depressed or not depressed at all. In a situation at a sports event, where perhaps many other people are bouncing you around, then it's a big difference.
A technical difference which does exist is that using AF-ON to focus, you can temporarily stop Servo AF from tracking but still take photos. If your target goes partly behind some obstructions, you can prevent the camera from re-focusing on the obstruction and sometimes still get shots, with some blurred out-of-focus obstruction covering only parts of the image.
That's impossible with AF on the trigger button.