The appearances of God, the angels and the saints to human beings on the earth fall into two general categories, apparitions and mysticism.
A mystic is a person who having persevered in the Christian spiritual life, usually a notable length of time, receives by God's free choice the infused supernatural grace of contemplative prayer. Through this grace they are granted a deeper knowledge and experience of God, beyond that which the ordinary ways of prayer and Christian life can give. This grace is usually granted after they have been faithful in avoiding sin, conquered themselves through mortification, and meditated faithfully on Christ and the truths of the faith taught by the Church. Passing through a profound trial known as the Dark Night of the Senses they enter upon the Illuminative Way, in which they make very notable progress in sanctity, as well as receive divine communications, whether of interior words (locutions) or interior (intellectual) or exterior visions. They may also experience ecstasies, levitations, the stigmata, and other signs of their growing intimacy with God and the supernatural. If they persevere on this path they will pass through another Dark Night, of the Spirit, in which their purification is completed. Entering upon the Unitive Way, their union with God is secured by a Mystical Marriage, prefiguring their union with God at death and the consummation of the union of Christ and His Bride at the end of time.
An apparition, however, is a charismatic gift granted by God for some greater purpose of His than the benefit of the one receiving it. It says nothing necessary about the sanctity of the recipient(s); although God usually chooses simple and good Christians, often children, who will readily accept and do His Will. Generally, it can be understood as an external vision, created by some means of God, to represent the holy person depicted. It would not necessarily have to be the person him or herself. Only Christ and Our Lady (possibly St. Joseph, according to St. Francis de Sales and others who hold that he was taken to heaven body and soul), could actually appear in their bodies. All others, and even they, could appear by some representation accessible to the human senses. In such a way God appeared by means of angels to Abraham and to Moses. According to St. Thomas Aquinas, this manner is the ordinary cause of mysticism and apparitions.
In the case of Fátima it is clear that something more than an intellectual vision took place, an external apparition accompanied by indications of the actual presence of Our Lady. This latter cannot be conclusively determined. However, it reasonably follows from the descriptions of the events and especially from the sense of Her Presence continued to be felt there to this day.
As a fruit of the events, and of the fidelity of the three children to the message of Fátima, Lucia, Francisco and Jacinta grew in holiness and became mystics in the proper sense. It is for their heroic virtue in the pursuit of God that the two youngest are being raised to the honor of the altar, not for being the recipients of an apparition. This fact, more even than the miracle of the Sun, authenticates the message of Fátima.
I am looking forward to seeing the new movie the 3th Day. ;-)