Hmm. Let’s see what the Church has to say about it.
[Redemptionis Sacramentum](
http://www.vatican.va/roman_curia/c...0423_redemptionis-sacramentum_en.html#Chapter VII) ¶¶ 156-58.
So, apparently, there is such a person (by definition a layman) as an “extraordinary minister of Holy Communion,” who fulfills the function of “extraordinary minister of Holy Communion,” and that person can be “appointed to this ministry” or not, according to the rules of the Church.
If a layman is appointed to be an extraordinary minister of Holy Communion, then that person fulfills the function of extraordinary minister of Holy Communion.
Please don’t expect the people in the Church to send out emails saying “We are in need of two more laymen to fulfill the function of extraordinary minister of Holy Communion for the 10:30 Mass this Sunday” when they could just as easily – and correctly – say “We are in need of two more extraordinary ministers of Holy Communion for the 10:30 Mass this Sunday.”
The term applies to the function
and to the persons appointed to fulfill that function. Both usages are clearly correct, as those are the usages the Church employs.