After sending the invoice to the customer if you want to send again the invoice there will be another email content. Becuase the initial invoice is already sent. Now the customer maybe want the invoice again and in all cases this content will be different. Go to Setup-> Email Templates -> Invoice Already Send to Client to edit the email content when sending the invoice to your customer for second time.
By default all contacts with enabled email notifications for invoices will be selected you can adjust to your needs.
When cron job will try to send the invoice eq. for expiration reminders will be sent to all contacts with enabled email notifications for invoices.