The Identity of Indiscernibles (hereafter called the Principle) is usually formulated as follows: if, for every property F, object x has F if and only if object y has F, then x is identical to y. Or in the notation of symbolic logic:
∀F(Fx ↔ Fy) → x=y.
Or, in more prosaic terms: If two objects share exactly the same set of properties, then they are the same thing.
But there's a dark side to metaphors. They're never quite exact. If they were they'd be the same thing. In some cases, those differences can lead us astray.