How bookings work — When you move or cancel one (2)
And the customer is told. A moved booking sends an email showing the old time struck through above the new one, because the first thing most people think is “was that always when it was?” If they gave a phone number they get a text too, naming both times, and it goes straight away even at night: a changed appointment can't wait for morning. A cancellation says who cancelled it. Both report back who was actually told — and where there was nobody to tell, because the booking carries no email, the scheduler says so rather than implying a message went out.
Cancel booking sets your own cancelled status, whatever you happen to call it, so the booking stays visible as a cancellation rather than disappearing. If your table has no such status the record goes to Trash, where you can get it back. Nothing here deletes anything for good.