There are a number of reasons that these three metrics may not match, and most are related to the deliverability of the items that you sent from Core iQ. In the platform, we do a check on all email addresses to make sure that they are properly formatted and appear to be valid. However, in certain cases an email will pass our filters and go on to SendGrid. This registers as a Processed item, but it does not get Sent because of the invalid email. This is typically the cause of a discrepancy between the Processed and Sent items. These items will usually be marked as Failed Processing.
The discrepancy between Sent and Delivered is purely on the end email holder's side. An item can be Sent but not Delivered if the email is completely valid, but the message bounced or didn't get correctly delivered to the end user. This is typically because of a full mailbox, an error on the email provider's side, or some other smaller issue. You can find all instances of items that didn't get Delivered correctly by searching for bad emails in the Email Outcomes report. Soft bounces (those that could possibly be successfully resent) are marked as a 'Bounce' in Core iQ's email metrics. Hard bounces (those that related to a permanently bad email) are marked as 'Dropped' in the metrics. Dropped items should prompt you to reach out on your end to the email holder, as that email will always fail. This is traditionally because the user no longer has an account at that provider, and is usually related to work emails for employees that are no longer at the company.
SENT = DELIVERED + BOUNCED + DROPPED