Does the address on my amended return have to be the same as the one that’s on my original return?

No, the amended return address does not need to be the same as the address on the original tax return that was filed.

Use the address where you want to receive mail from the IRS.   If you are getting a refund for the amended return, the IRS will only mail you a check.   You will want that check to go to your current address.