Pill confusion

My friends and I have been very confused about some rules with the pill. These were never gone over with us at our doctors. So I know that when you’re starting a new form of birth control you have to wait a week for it to start working. What we all have confusion on is: after you finish a pack (placebos too) and start your new pack on the correct day, will you still be protected on day 1 or do you have to wait a week like when you first started the pill to be protected?