If the engine has failed, then one doesn't really care that it failed for a fuel pump failure or of the accessory drive shaft has failed; it's simply failed. Unless there's a sign severe damage, there's no reason to treat the engine for severe damage.
That the engine has been damaged internally in a severe way isn't relevant; the actual damage that has occurred isn't important; how it affects crew operation is what's important.
The severe damage checklist is a ballpark catch-all for a big, immediate problem. On our checklist, it's called the Engine Fire/Severe Damage/Separation checklist; it's for handling multiple contingencies, and the only immediate action item on the list is the same for all three possibilities: maintain control of the airplane. The items which follow involve control of the airplane issues, then fire issues, then system issues (hydraulic, electrical, etc).
The actual cause of the severe damage isn't so important as what to do about it. If you've got a real problem that doesn't fit any particular other definition and it's vibrating, then it's severe damage.
If the accessory drive has failed and the engine has flamed out, then one has an Inflight Engine Failure/Shutdown checklist, instead. (Our procedures also call for this checklist in the event of vibration).
If a specific failure is identified that matches any one of the other procedures, then use that. If you've got a real problem without a specific definition, you've got the severe damage checklist.