Well, apparently the bishops of Scotland haven’t clue on how to answer a simple Master of Divinity question on the difference between the “lay apostolate and lay ministry” either, until today when Pope Benedict let them know a little secret:

Hand in hand with a proper appreciation of the priest’s role is a correct understanding of the specific vocation of the laity. Sometimes a tendency to confuse lay apostolate with lay ministry has led to an inward-looking concept of their ecclesial role. Yet the Second Vatican Council‘s vision is that wherever the lay faithful live out their baptismal vocation – in the family, at home, at work – they are actively participating in the Church’s mission to sanctify the world. A renewed focus on lay apostolate will help to clarify the roles of clergy and laity and so give a strong impetus to the task of evangelizing society.

from Pope Benedict XVI’s Ad Limina Address to the Bishops of Scotland

What is meant by the term “ministry”? John Paul II said, “The language becomes doubtful, confused and hence not helpful for expressing the doctrine of the faith whenever the difference ‘of essence and not merely of degree’ between the baptismal priesthood and the ordained priesthood is in any way obscured.” In another place he said, “Only in virtue of sacred ordination does the word [ministry] obtain that full univocal meaning that tradition has attributed to it. There is an urgent pastoral need to clarify and purify terminology, because behind it there can lurk dangers far more treacherous than one may think. It is a step from current language to conceptualization.”

If you want to know, read the following:

Pope John Paul II, Christifideles Laici (1988)