Mishnayos Horayos Perek 3 Mishnah 4

And who is the anointed priest? It is the High Priest who is anointed with the anointing oil, not the High Priest consecrated by donning multiple garments, i.e., one who served after the anointing oil had been sequestered, toward the end of the First Temple period. The difference between a High Priest anointed with the anointing oil and one consecrated by donning multiple garments unique to the High Priest is only that the latter does not bring the bull that comes for the transgression of any of the mitzvot. And the difference between a High Priest currently serving in that capacity and a former High Priest who had temporarily filled that position while the High Priest was unfit for service is only with regard to the bull brought by the High Priest on Yom Kippur and the tenth of an ephah meal-offering brought by the High Priest daily. Each of these offerings is brought only by the current High Priest, and not by a former High Priest. Both this High Priest currently serving and that former High Priest are equal with regard to performing the rest of the Yom Kippur service, and they are both commanded with regard to marrying a virgin (see Leviticus 21:13), and it is prohibited for both to marry a widow (see Leviticus 21:14), and they may not render themselves impure with impurity imparted by a corpse even in the event that one of their relatives dies (see Leviticus 21:11), and they may not grow their hair long and they may not rend their garments as expressions of mourning (see Leviticus 21:10), and when they die they restore the unwitting murderer to his home from the city of refuge (see Numbers 35:25).