Disney's been moving to serving nuggets, not fingers. They're also moving toward offering grilled chicken over fried.
The nuggets, as mentioned above, are the same chicken as the fingers or strips - except for the children's menus, which apparently include formed processed nuggets, not breast meat nuggets.
The only TS with chicken fingers on an (unofficial) child's menu that I know of is Olivia's. You may also wish to look up menus on restaurants at DTD and the Swan/Dolphin, as those restaurants are not owned by Disney and don't use Disney's standardized menus.