What is invoicing
An invoice is a formal document requesting payment for goods or services provided, outlining the details of the transaction.
An invoice can be created by you manually creating on in Beyond Classes --> Invoicing or right before a subscription renewal. An invoice "opens" when you manually send an invoice to a customer or right before a package or subscription is charged.
Every time your customers have a subscription an invoice is created ~1 hour before automated attempts to process the payment through the customer's default payment method charge the invoice.
What are payments
Payments update in response to actions taken by the customer when trying to pay the invoice. Each invoice has a payment that is associated with it.