We hold to the traditional threefold ministry of the Apostolic Church: Bishops, Priests, and Deacons.
The diocese I joined the Episcopal Church in had only transitional deacons -- just like in Catholicism, people who are serving a term in the Diaconate before being ordained to the Priesthood. The one I'm in how has vocational deacons who serve in a number of roles throughout the diocese. A friend of my wife's is a deacon who is head (and half the staff) of a Disability Advocacy ministry headquartered in Greensboro, NC. (I.e., people who serve professionally as advocates and paper-pushers for the disabled, particularly the mentally disabled who need assistance in showing that they qualify for SSI and such.)
Nearly all Episcopal parish churches call rectors who are the equivalent of Catholic pastors. Small mission churches get vicars or join themselves with other churches in "clusters" which together employ a rector. The larger churches have two or more priests serving them; formerly any priest assisting the rector was a curate, but the tendency lately has been to identify their roles with titles that are appropriate. The church we attended in Watertown was at one point headed by a man who excelled in preaching and administration but was poor at pastoral care, and knew it. He therefore had the Vestry employ another priest who was the Pastoral Associate, with primary duty for providing pastoral care. My own church is served by a married couple, one of whom is Rector and the other Associate Rector -- they look on their work as a team ministry, operating as equals except for the rare occasions when the legal authority of the Rector is required.
Bishops are heads of dioceses, of course, with a very few in other roles. In addition to the diocesan bishop, there are three other categories of bishops working in dioceses:
1. When the diocesan bishop is contemplating retirement from full-time diocesan ministry and authority, he informs the diocese of his intent, and they elect a
Bishop Coadjutor, who assists him while learning the ropes until he retires, and then succeeds as diocesan.
2. Larger dioceses will have one or more
Bishops Suffragan, who are assistants to the diocesan bishop, with no right of succession. (They may of course be chosen by other dioceses as their new diocesan bishop.)
3. Retired bishops will often work part-time on an ongoing basis or fill in on an emergency basis as
Assistant Bishops. (E.g., Pittsburgh needs about 1 1/2 bishops' services, and they have a half-time Assistant. A diocese where the diocesan or suffragan dies suddenly or becomes critically ill will have a retired bishop step in to help carry the load.)
4. I should mention that we have a Presiding Bishop who is the chief executive for the church as a whole, without diocesan duties but with a broad range of program responsibilities and the duty to attempt to "herd cats" by speaking with authority to the national church as a whole. He is explicitly not an Archbishop, and does not have the power of the metropolitan, as in the Catholic and Orthodox churches and in some branches of the Anglican Communion (the Church of England, Canada, Australia, and Wales have Archbishops who are metropolitans). [This is the reason why the ordinary of a diocese is not the suffragan as he is in Catholicism, but rather his assistant if there is one.]
We call men and women, single or married, to the diaconate, the priesthood, and the episcopacy. The first woman diocesan bishop of our church, in Vermont, just retired a year ago. And last year's General Convention added to our calendar of saints the first woman ordained priest in the Anglican Communion,
Florence Li Tim-Oi.
We like to think that all our ministers are extraordinary!
But in the sense you're asking, yes, there are laymen set apart to administer the Eucharist.
My wife is a Chalice Bearer licensed by the diocese, who has felt called to that ministry, and trained for it. In this diocese, each church is authorized a specific number of chalice bearers based on the number of communicants.
Our parish has five Lay Eucharistic Ministers to the Ill and Infirm, whose duty it is to take the consecrated elements to the sick and shut-ins as needed (most Sundays there is at least one person needing this ministry) and lead a brief service based on the form for Communion Under Special Circumstances (p.398 BCP). The Priests of course will also visit the sick and deliver communion, but having lay parishioners do it as well emphasizes that the visitation is in behalf of the parish, not the private ministry of the priest to the individual.
In our parish, there is one man authorized to administer the bread when insufficient priests are available to administer communion in a timely manner. I believe this is standard practice to have someone on hand in an emergency.
(We were friends with Ed, an elderly Lay Reader/Chalice Bearer in upstate New York who may have been the only layman ever to validly and licitly read the Eucharistic Prayer in a formal church service. He was assisting a priest handling services at a small rural church where he (Ed) read Morning Prayer on most Sundays and the priest celebrated the Eucharist every few weeks -- and the priest had laryngitis and lost his voice during the Liturgy of the Word. So Ed read the Eucharist aloud while the priest celebrated
sotto voce, performing the manual acts and reciting the Eucharistic Prayer quietly as best he could!
)