Personally, I believe a register should be used for all failures be they a nonconformance or a noncompliance. When you start having more than one tool, the users start getting confused or lose their interest/engagement in the system.
I have seen some failures that were of a sensitive nature and the process owner felt that the details should not be seen by all employees. In a situation like this, the register was used to record the failure, but the details and associated paperwork were protected from the general population.