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No, ETC guns are not related to coil guns or rail-guns at all. The only thing like them in fiction are the plasma explosion driven Naval Autocannons from battle-tech, except ETC guns use plasma to ignite conventional propellant rather than on its own.

I suspect the lack there of is probably what tanked the project.

Given what it is trying to do, I bet the research on plasma injectors that General Fusion is doing will have some benefits into filling those holes.