Horayot 11 - How is Anointed High Priest Different
An anointed High Priest is installed into his office by being anointed with the special oil prepared by Moses, and by donning four extra vestments in addition to the four garments of the regular priest. After the anointing oil was concealed, only the installation by donning the extra vestments remained.
The difference between an anointed High Priest and one who was installed with additional garments is that only the anointed Priest brings a special bull sacrifice if he sins or the court errs.
If a High Priest becomes ritually impure or otherwise temporarily unfit for service, another High Priest is appointed in his stead. When the first one returns, he is called The Serving High Priest, and the temporary substitute gets the name of High Priest Who Passed out of Service. The Serving High Priest is higher in that he brings the bull of Yom Kippur and his daily flour offering. They are equally commanded to marry a virgin and cannot marry a widow. Both cannot observe mourning, and accidental murderers return from their exile on the death of both.
Art: James Jacques Joseph Tissot - A Widow