The Extraordinary in the original Vatican 2 document did not refer or mean the lay person it meant and means the circumstances in which a lay person might distibute the sacred species so the words are used separate and distinct from each other, no oxymoron.
But the term “Eucharistic Minister” refers exculsively to the Sacrament of the Eucharist.
Every Sacrament has a Minister, the one who confect the Sacraments, or brings about it’s reality.
The Minister of Baptism is the person who pours the water while reciting the Triune Formula. This can be done by a priest or deacon ( the Ordinary Ministers) or, in cases of emergency by a lay person. Baptism, therefore does have an Extraordinary Ministery.
In the Sacrament of Confirmation, the Ordinary Minister is a Bishop ( in the Latin Rite). The Extraordinary minister is a priest with faculties to do so.
In the Sacrament of Marriage, the Ministers of the Sacrament are the couple themselves. There is no Extraordinary Minister of Matrimony.
In the Eucharist, the Minster of the Eucharist is a bishop or validly Ordained priest. The Ordinary Ministers of the Sacrament are bishops and priest in the clerical state. The Extraordinary Minister of the Eucharist is a laicized priest (one removed from the clerical state), the can confect the Eucarish in extraordinary circumstances.
An unordained lay person cannot, by definiton, be a Minister of the Euchrist ( or it’s liguistic equialent a Eucharistic Minister).
They can, however bring the confected Eucharist to the community. That is a seperate ministry, can the Minister of Holy Communion. The Ordinary Minister of Holy Communion is a cleric in Holy Orders ( deacon, priest, bishop). They role may, in certain circumstances, be delegated to the laity. Such a person is called an Extraordinary Ministery of Holy Communion, or EMCH for short.