We would just say a seized rotor for core lock. I may try introduce core lock as a term in our business though as we call a turbo without end housings a turbo core.
Coking is the term used to describe the oil that has carbonised on the components due to the high temps. It looks like black powder but is nigh on impossible to get off of the parts when formed and acts as an abrasive. once it's there it's there for good and only gets worse :D
Moral of the story... Don't do hot shutdowns with turbos or turbofan engines, especially those in the next DCS A-10C patch (or which ever the feature it is included in :D )