Are inertial and gravitational energy the exact same thing

Or are there subtle/not too subtle differences?

Hum, I'd say no. There's a little 'query' upon inertial and gravitational mass, but in terms of energy, I think the question has no sense. Gravitational energy is potential energy, it affects a body's motion, while it 'inertial energy', which I interpret as the rest mass, do not affect it's motion, only its ability not to move.
If your question was in terms of mass, I think we could say with some certainty that they're the same thing, given the very accurate experiments that were done throughout the history of physics.