I would like to have more context about the use of the two words. Nevertheless I will try to give an explanation. Nonconforming output is related to the non-compliance with a specification associated with a final or intermediate product or service. Nonconformity can be used in the same context as nonconforming output or, more generally, whenever there is the non-fulfillment of a requirement of a management system. For example, a company did not performed the re-evaluation of its supplier base as scheduled.
The following material will provide you information about nonconformities: