What is the difference between Symbolism and Abstract thinking in Piaget's Theory?
Symbolism uses a symbol to represent an existing object, while abstract thinking can be thought of as considering things that don't actually exist. 

For a rough example of each, consider representation as symbolism (this paper is the plane I'm on) and consider generalization as abstraction (what it means to be "on" something). For another, consider something (this blue line on a paper) that represents something else (this river), contrasted with considering the concepts of "blue" or "line".