Megillah, Chapter One, Mishnah Nine
Our mishnah deals with differences between different types of high priests.
There is no difference between a priest anointed with the oil of anointment and one who [only] wears the additional garments except for the bull which is offered for the [unwitting transgression of] any of the commandments.
There is no difference between a serving [high] priest and one whose time has passed except the bull of Yom HaKippurim and the tenth of the ephah.
Section one: The high priest was supposed to be anointed with special anointing oil, except that the composition of this type of oil was unknown in the Second Temple period and hence not used. The distinction in the Second Temple period between high priests and ordinary priests was that the high priest had eight garments and the ordinary priest wore only four. Our mishnah teaches that the difference between the high priest in the First Temple and the high priest in the Second Temple is that only the anointed priest brings a bull for an unwitting transgression, as is stated in Leviticus 4:3, If it is the anointed priest who has incurred guilt
Section two: The high priest who is currently serving in office brings the sacrificial bull on Yom HaKippurim (Leviticus 16:6) and the tenth of an ephah of flour offered every day (Leviticus 6:13). Otherwise a high priest who has been removed or otherwise left office is treated the same as the currently serving high priest. For more information on this, see Horayot 3:4.