The Recurring Invoice functionality has been discontinued for new Partners. Please familiarize yourself with the enhanced Subscription Billing feature, which has been introduced as a replacement.
A recurring invoice template is used to set up the schedule for which an invoice is generated. The recurring invoice template captures the products, price, recipient, payment method, and the recurring schedule (weekly, monthly, yearly, etc).
An invoice is an actual output that is generated at end of every schedule, that is sent to bill the customer.
Simply put, a monthly recurring invoice template will generate an invoice every month.