The Term "Priests"

Roman Catholics, Episcopalians and Orthodox Christians, and most non-Abrahamic religion clergy are called "priests", but clergy in most Protestant Christian denominations, who are doing essentially the same job as priests in Christian denominations that have priests, are usually called pastors or ministers. 

In the case of Episcopalians a.k.a. Anglicans, the linguistic detail is a litmus test in a denomination that does not consider itself to be unequivocally Protestant, for some purposes.

A few Christian denominations, of course, don't have professional clergy, although most are small.

Judaism has a "priest" concept (the Aaronic priesthood, not to be confused with the Mormon religious institution of the same name), but except among Samaritans and some Ethiopian Jews, the term isn't used for its primary professional clergy members who are called "rabbis" (i.e. teachers), and Jewish "priests" are largely a vestigial trapping left over from the sacrificial offering oriented Temple Judaism phase of the Hebrew religion preceding the modern Rabbinic Judaism that arose following the destruction of the Jewish temple in 70 CE. Instead, it refers primarily to Jewish laymen who as a hereditary matter has some minor additional religious duties and obligations as part of their ordinary daily life.

As far as I know, there are no religious officials with the title "priest" in Islam. The closest analog to a "priest" in Islam is an Iman, although independent Islamic religious scholars also play an important part in grass roots religious life for Muslims.

Other questions

Is a bishop or archbishop or cardinal or Pope also a "priest" or are those terms mutually exclusive? 

Are monks and nuns ever priests, or are those terms for members of religious holy orders also mutually exclusive? 

Both of those answers, I acknowledge, may be denomination specific. For example, in some religious denominations that are organized democratically, the terms "bishop" and "archbishop" refer to non-clergy who hold governance roles in the denomination.

Are there any Christian denominations that have the clerical title "high priest" or is the title "high priest" used exclusively for non-Christian clergy?