CRI means Certification Review Item, CAI means Certification Action Item

The CRI Process is used during a certification project for structured discussions about technical details and applicable regulations, certification specifications, interpretations and acceptable means of compliance. The result of a CRI will be an agreement between applicant and EASA. The solution is e.g. the certification basis, a special condition, acceptable means of compliance, etc.

CAIs are defined actions within a certification process that are numbered for traceability.
A CAI should be clearly defined and not a matter that requires discussions.

This is a quick overview that is not considered comprehensive. I hope it helped.

Check document WI.CERT.00146-001 on EASA website

Can you tell me how they are related Certification Action Item with Compliance demonstration items [CDI]?