How does the core relate to strong equilibrium? An allocation is in the core if there's no coalition that blocks it.

A strong equilibrium (Aumann, 1959) is a Nash equilibrium in which no coalition, taking the actions of its complements as given, can cooperatively deviate in a way that benefits all members of the coalition.

How are these distinct? I usually don't think of the core as a solution concept, but I'm struggling to disentangle it from strong equilibrium.
Strong Nash equilibrium is different from core mainly because of communication. In a Strong Nash, unlimited private communication is allowed. The core is a concept that is linked to Coalition-proof Nash equilibrium rather than Strong Nash. People can freely communicate but cannot make binding commitment before deciding.

In some games, both happen to be the same, but in generality, the core is a concept derived from Coalition-proof Nash equilibrium rather than from Strong Nash Equilibrium.