In our experience, at CS locations and a la carte TS, the child has to eat off your plate or you can order a meal for them and pay out of pocket.
For buffets, you can make the child his/her own plate of anything and not be charged. At buffets, we were universally offered a drink free of charge for our son when he was under 3 (they also brought out several cupcakes for him during our trip since he was turning 3 on the trip)
At Ohana, at least, which is AYCE served family style, our son was welcome to eat any of the standard offerings BUT they also offered to bring him some kid fare (chicken nuggets) and didn't charge. [Other DISers have reported that places like CRT will offer something for the little ones.]