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What is the difference from CA perspective between renewal and rekeying of the certificate previously issued by this CA?

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From RFC 3647: Internet X.509 Public Key Infrastructure -- Certificate Policy and Certification Practices Framework:

4.4.6. Certificate Renewal

This subcomponent is used to describe the following elements related to certificate renewal. Certificate renewal means the issuance of a new certificate to the subscriber without changing the subscriber or other participant's public key or any other information in the certificate:

  • Circumstances under which certificate renewal takes place, such as where the certificate life has expired, but the policy permits the same key pair to be reused;

Which contradicts itself in that it initially states that during renewal you cannot change the public key or any other information in the certificate, but then goes on to say that a renewal can take place where the certificate life has expired.

and...

4.4.7. Certificate Re-key

This subcomponent is used to describe the following elements related to a subscriber or other participant generating a new key pair and applying for the issuance of a new certificate that certifies the new public key:

  • Circumstances under which certificate re-key can or must take place, such as after a certificate is revoked for reasons of key compromise or after a certificate has expired and the usage period of the key pair has also expired;
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  • Not sure there's a contradiction in the way you're thinking. Sure, if you count notBefore and notAfter as "information" in the certificate, one could read it as a contradiction, but in the classical sense, this is simply a limitation on lifetime, and doesn't confer any information as to the certificates capabilities or cryptographic restrictions. For example, a renewal of a certificate shouldn't add or remove a Key Usage/Extended Key Usage attribute, change the DN, or add extra SubjectAltName aliases. Performing any of these actions is a reissuance rather than a renewal.
    – Tyzoid
    Jul 16, 2022 at 20:44
  • @Tyzoid - I couldn't agree with you more. It's an academic argument whether lifetime counts as information, or as you say, a limitation on lifetime. At a push, the RFC could have been worded better maybe?
    – garethTheRed
    Jul 17, 2022 at 6:47
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Here's a quote from Symantec's Certificate Policy statement:

Generally speaking, both “Rekey” and “Renewal” are commonly described as “Certificate Renewal”, focusing on the fact that the old Certificate is being replaced with a new Certificate and not emphasizing whether or not a new key pair is generated.

Then they define Rekey and Renew as (emphasis mine)

Certificate renewal is the issuance of a new certificate to the subscriber without changing the public key or any other information in the certificate. Certificate renewal is supported for Class 3 certificates where the key pair is generated on a web server as most web server key generation tools permit the creation of a new Certificate Request for an existing key pair.

Certificate rekey is the application for the issuance of a new certificate that certifies the new public key. Certificate rekey is supported for all certificate Classes.

Really just comes down to policy. A CA could decide that it will always prohibit issuance of a certificate using a key already certified. Having (and enforcing) that policy requires a more expensive issuance process than merely verifying that the subject identification material is valid, since they would need to compare the public key to all previously issued certificates.

The CA/Browser Forum's Baseline Requirements has no stipulations for renewal or re-key (sections 4.6 and 4.7), and the Extended Validation requirements don't seem to mention the keys.

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