Q. 1. Is it proper to call a layperson a "Eucharistic Minister" because he distributes Holy Communion during the Holy Mass?
A. 1. In the Roman Catholic Church, the only minister of the Eucharist is the priest. [Redemptionis Sacramentum, # 154-5]
"As has already been recalled, “the only minister who can confect the Sacrament of the Eucharist in persona Christi is a validly ordained Priest”. Hence the name “minister of the Eucharist” belongs properly to the Priest alone. Moreover, also by reason of their sacred Ordination, the ordinary ministers of Holy Communion are the Bishop, the Priest and the Deacon, to whom it belongs therefore to administer Holy Communion to the lay members of Christ’s faithful during the celebration of Mass. In this way their ministerial office in the Church is fully and accurately brought to light, and the sign value of the Sacrament is made complete." [Redemptionis Sacramentum, # 154]
"In addition to the ordinary ministers there is the formally instituted acolyte, who by virtue of his institution is an extraordinary minister of Holy Communion even outside the celebration of Mass. If, moreover, reasons of real necessity prompt it, another lay member of Christ’s faithful may also be delegated by the diocesan Bishop, in accordance with the norm of law, for one occasion or for a specified time, and an appropriate formula of blessing may be used for the occasion. This act of appointment, however, does not necessarily take a liturgical form, nor, if it does take a liturgical form, should it resemble sacred Ordination in any way. Finally, in special cases of an unforeseen nature, permission can be given for a single occasion by the Priest who presides at the celebration of the Eucharist.  [Redemptionis Sacramentum, # 155]
"This function is to be understood strictly according to the name by which it is known, that is to say, that of extraordinary minister of Holy Communion, and not “special minister of Holy Communion” nor “extraordinary minister of the Eucharist” nor “special minister of the Eucharist”, by which names the meaning of this function is unnecessarily and improperly broadened." [Redemptionis Sacramentum, # 156]
Origin of this abuse
The phrase "Eucharistic minister" has, however, sometimes been used inaccurately to refer to an extraordinary minister of Holy Communion.
In the Anglican Church the term Eucharistic Minister is used to denote someone who assists the priest in administering the bread and wine. Often this is in the form of the wine, but once licensed, a Eucharistic Minister is licensed to administer in both kinds (namely both the bread and the wine).
A further role of the Eucharistic Minister in the Anglican Church is for them to administer home communion to the sick and housebound. In some Anglican churches Eucharistic Ministers will take intinctured bread (bread from the communion table that has had a drop of blessed wine placed on it) directly from the communion services to housebound communicants in the surrounding area.
It is obvious from the aforementioned that many Catholic Dioceses have embraced Anglican terminology that has never been approved by the Vatican.