C - P = S - K e^(-rT).
What makes it special: it follows purely from replication and holds regardless of volatility, drift, or the return distribution. A call plus discounted cash and a put plus the stock pay identically in every future state, so they must cost the same today.
Any pricing model must respect it, and a violation is a genuine arbitrage.
The nuance. For American options it becomes an inequality, because early exercise is possible on the put.