How to match Distributions with respective Contacts, what field to merge on?

We are getting Distribution Data from List Distributions End Point which gives us 'recipients.contactId'
and now we want to match these with the Contacts data that we got from List Directory Contacts endpoint
which has a 'contactId' field. But when we join these two data on 'contactId' = 'recipients.contactId'
we dont seem to have any match which is weird. For reference, all the values in 'contactId' in List Directory
Contacts end point starts with 'CID_' but the values of 'recipients.contactId' from List Distributions end point
starts with values like 'CTR_' or some other values. We have also tried removing the first 4 characters and joined
both the data, still no success. Any help on this would be really helpful.