Hi,
820 remittance is electronic payment by an org to its vendor. So its direct bank to bank transfer. There is no check involved.
823 file received is check payment from customers through a bank. Customer sends a physical check to bank. Bank will collect the info in the check and send an 823 file to the organization.
From your statement above I believe you are thinking that 820 remittance from an org to a vendor should have the same info as 823 file received by the customer.
You cannot compare the 2 and SAP does not reconcile 820 and 823. There is no process in SAP. Hence you need to revisit your assumption on the observation you have made.
Regards,
Avinash