difference between disatnce protection and differential protection

Distance protection, typically applied on transmission lines, measures the impedance of the line by a VT and CT input from one end of the line to the relay and responds to under impedance. Simply put, a line will have a definite value of impedance for a particular length in ohms and a fault along the line will result in a reduction of this value. Settings are zones, usually in ohms as a percentage of the line's impedance. Differential protection, on the other hand, is a unit protection that has CT's on either end of the line and works on the current balance principle. A fault within the protected zone, the length of the line, will result in an imbalance of sending end and recieving end current (i.e. an alternative path of current flowing to the fault). The currents on either end are compared by two identical relays which communicate by pilot wire, optic fiber, microwave or power line carrier comms channel. Differential protection is also applied to generators and transformers.

Post -1 above has given you a fairly good idea of the difference between the two. For detailed understanding please go through the Book "Protective Relaying (Principles and Applications) by J Lewis Blackburn", this is considered to be the bible on protection relays.