Schedule of non-current asset and non-current assets register

Hopefully you are clear on what the non-current asset register is https://opentuition.com/topic/non-current-asset-register

You would have to consider the context to know what is meant by “schedule” of non-current assets. This could be a client’s working paper which summarises the totals of costs and accumulated depreciation by class of asset for agreeing to the account balances in the general ledger.
Or it might take the form of a reconciliation of opening to closing carrying amounts (which is a disclosure requirement for the notes per IAS 16).

You would expect these schedules to be included in the audit working papers – e.g. see s.1.4
in Chapter 22 of the Study Hub for an illustration https://www.accaglobal.com/uk/en/student/your-study-options/studyhub.html