Probably an obvious answer, but I could not find anything about this in the manual. What is the difference between selecting after report production or after report delivery in a task?

I have a package that runs, saves some reports to the disk, then emails them. I have a task that kicks off another package, so if I select after production, it will kick off after the reports run, and if i select delivery, it will kick off after the reports are copied and emailed? What is more efficient if I have several packages kicked off using this method?

You are right. With "after report production" the task will run (kick off) after the production of the reports and with "after report delivery" it will be after the report delivery. On efficieny it sounds like a good case for event based schedules, I would think it would be dependent on what the schedules that are kicked off need and do and perhaps if you have access to the multithreading feature? this is interesting, please share what you find works for you

If you use report delivery instead of report production then CRD will not run the task till the report has been delivered. So, for an email, for example, if the mail server goes down, the report will not be delivered for a while, so the task won't kick in till the delivery has been successful.

If you use report production, the custom task will run as soon as the export is completed. CRD won't wait for the delivery stage and the task is not dependent on whether the report has been delivered or not.

I don't think one method is more efficient than the other. It is purely a questions of your business requirements, I would think.