What is the difference between Automatic and Manual collection methods?

Automatic invoices will bill immediately upon creation using any stored payment method saved on the customer's Recurly account.

Manual invoices can have due dates set further in the future and allow you to send customers their invoices and either have payments made outside of the system recorded against it to have it marked as paid, or the customer can add a payment method to their account and make a payment online for the invoice as well.