Send me a copy, in the Send panel, is ticked to start with: you get the same email as Bcc, so you have it and know it went out, and the invoice's Activity lists your address.
Send now asks first, naming the addresses the email will go to and, for a draft, saying its details will become final.
In the app, Send has the same To, Bcc, Send me a copy, subject, message, reminders and Send test to me as the website, and an invoice shows its Payment reminders with a switch to turn them off or on.