Full Idea
Leibniz's Law ('if identical, must have same properties') defines identity according to the properties possessed by the object itself, but the Identity of Indiscernibles defines identity in terms of how things are conceived or grasped by the mind.
Gist of Idea
Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects
Source
J Baggini / PS Fosl (The Philosopher's Toolkit [2003], §3.16)
Book Reference
Baggini,J and Fosl,P.S.: 'The Philosopher's Toolkit' [Blackwells 2003], p.100
A Reaction
This is the heart of the problem of identity. We realists must fight for Leibniz's Law, and escort the Identity of Indiscernibles to the door.