The Catholic Church (and apparently Lutheran, Anglican and Episcopalian churches) have clergy with the title of "priest", as did Old Testament Judaism. Are Protestant "preachers", "reverends", "pastors", "ministers", etc. all essentially "priests", or is there some difference between these two systems of clergy titles? Why didn't Protestants just keep on with the title "priest" for it's clergy? Why does Catholicism not follow the same logic and avoid that title?
In the Old Testament, priests would appeal to God on behalf on sinful men through sacrifices. Jesus is the Great High Priest who 1) offered Himself as a sacrifice once for all and 2) who ever lives to intercede for us.
The old priesthood order was of the line of Aaron, but in 70 A.D. in the destruction of Jerusalem, the ancestral records were destroyed, I believe. Therefore, there is no current Aaronic Priesthood. Jesus was of the greater Melchizedek Priesthood that preceded the Aaronic Priesthood.
Consequently, there is no need for a man to intercede on our behalf to God, since Jesus does that. Indeed, the New Testament states that there is "one mediator between man and God--the Man Christ Jesus".
The New Testament also states that all believers are priests (a chosen priesthood) to worship God.
The role of priest is not mentioned in Ephesians 4:11-12
It was he who gave some to be apostles, some to be prophets, some to be evangelists, and some to be pastors and teachers, to prepare God's people for works of service.
The Protestant church has the office of pastor and teacher and evangelists. Missionaries could be considered apostles, since that word means "one who is sent out". Teaching pastors could be considered prophets--not necessarily in foretelling the future, in proclaim the message of God.
So, Protestants reject the notion that there is the need for any other mediator between us and God. We confess our sins to God--not to any man. (Only one place in the New Testament are we commanded to confess sins to another person, and it states there that is "to one another"--not to a priest. So, confessing to a "priest" is valid if the "priest" confesses to you as well).
Protestants believe in a concept called the "priesthood of all believers". Check out Wikipedia's article on the Universal priesthood.
The basic belief is that each Christian has the authority to preach and teach, read and interpret the Bible, and confess their own sins directly to Jesus. We still have professional clergy, but without formal sacraments to administer and with the authority individual lay-people have their functions are essentially to oversee the teaching of the church and run its ministries.
The bottom line is Protestants do not believe in a priesthood in the sense that the Roman Catholics, Eastern Orthodox, or OT Jews do/did.
In addition, according to the instructions of God to the priesthood of the lineage of Aaron, their was a veil in the temple seperateing the "Holy of Holies" where only the priest was allowed to enter into the presence of God. As stated, he did this on behalf of others.
Matthew 27: 51 tells us that immediately following Christ yielding His spirit to death on the cross, "Then, behold, the veil of the temple was torn in two from top to bottom;. . ."
Protestants believe that this was an act of God, as the veil was extremely thick and extremely tall thus the tearing was not possible by man. We believe this act to symbolize the new access to every believer granted by Christ's sacrifice of Himself on our behalf. He then became the ultimate and only Priest or go-between or mediator for each of us and God.
Also, Hebrews 4:15-16 "For we do not have a High Priest who cannot sympathize with our weaknesses, but was in all points tempted as we are, yet without sin. Let us therefore come boldly to the throne of grace, that we may obtain mercy and find grace to help in time of need." Again, because Christ understands and sacrificed Himself for our weaknesses and has already made the believer's acceptance known to God, we can boldly access God's throne, no earthly middleman requrired.
In the same way Christ took the place the priest, He took the place of the blood of the sacrifice and the sacraments of the OT. Thus, the pastors, spiritual leaders, of most Protestant churches duties are substantially different from those of the priest; no requirement for the hearing of confessions, although confession one to another, parishioner and pastor alike, for accountability sake is oft times good for the soul and beneficial to ones growth; no dictating retribution, sins are confessed directly to God and reconciliation between God and the believer a personal path God and he/she take together, without dictation from, or most often even involvment with the pastor.
And, as is noted, priest is not listed in Ephesians 4 as a spiritual leader title. Pastor and teacher are.
The Catholic faith celebrates 7 Sacraments. Most Protestant faiths celebrate 2, although they do not call them sacraments, but ordinances. Some Protestant faiths that celebrate a liturgical form of practice like the Catholic church also celebrate more than 2. Sacraments are outward signs that give inward holiness or grace to the soul. Sacraments are just another way that God conveys His love to us as God loves to use matter to convey His love.
Catholics believe that we are all called to be Priest, Prophet and King thru our Baptism. We call this the "common priesthood".
We also believe that certain men are called by God to continue the mission entrusted by Christ to His apostles to be exercised thru His Church until the end of time. We call this the "apostolic ministerial priesthood" in which there are 3 degrees: episcopate, presbyterate and diaconate.
Everything that the priesthood of the Old Covenant prefigured finds its fulfillment in Christ Jesus, who is the one mediator between God and men. The redemptive sacrifice of Christ is unique accomplished once for all, yet made present in the Eucharistic sacrifice of the Church as Jesus said at the Last Supper as He held up the Bread and Wine, "to do this in memory of me". The same is true of the one priesthood of Christ, it is made present thru the ministerial priesthood without diminishing the uniqueness of Christ's priesthood: "Only Christ is the true priest, the others are only His ministers of faith".
Cateechism of the Catholic Church, paragraph 1547.
The Catholic Church also uses the name Pastor when referring to Her priests and also considers Protestant Pastors to be Jesus' ministers of faith as well.
You could argue about the Bible terminology, as the answers above have done, but I think you would miss the main difference.
It stems from one of the main points of contest between the churches: the value of aesthetics. A priest is the master of ceremonies. He performs rituals. Protestants began by believing that rituals should be simple and minimal, so as to not become a distraction to the true purpose of faith. A minimalistic ritual can be performed by any member of the church, and so there only remains a need for teachers and worship leaders.
Catholics (also Anglicans and Orthodox), on the other hand, do not think they are distracted by lush performances, and so they have a person well trained in making such happen.
I think all the above answers, while offering interesting insights, confuse the meaning of the word priest, making one into a mediator between man and God, and thus accusing the other side of being disconnected from Him.