In general, when an insurance company rejects a claim, they are not keeping a record of that claim in their adjudication department. When they deny a claim, they still have a record of that claim in their adjudication department.
Rejections (when the claim was submitted electronically) usually come back as an EDI Rejection (electronic claim error) and will not show up on an Explanation of Benefits or Electronic Remittance Advice that you receive from the insurance company.
Denials normally come back on an Explanation of Benefits or Electronic Remittance Advice (ERA).
If the claim was rejected, in general, you can resubmit the claim (because they do not keep a record of the original submission in their adjudication department).
If the claim was denied, in general, you would need to send a corrected claim. If a claim was denied and you resubmit the claim (as if it were a new claim) then you will normally receive a duplicate claim rejection on your resubmission.