I don't see how purification can be equated with punishment.
Of course Catholics do not believe any more that purgatory entails
any punishment for temporal punishment due to sin. What a thought!
That previous Catholic teaching has been banished back to the Dark Ages.
There is such a teaching in the Baltimore Catechism but it is outdated now and believed only by some of the older Catholic generations.
Q. 853. How does the Church by means of Indulgences remit the temporal punishment due to sin?
A. The Church, by means of Indulgences, remits the temporal punishment due to sin by applying to us the merits of Jesus Christ, and the superabundant satisfactions of the Blessed Virgin Mary and of the saints; which merits and satisfactions are its spiritual treasury.
The online Catholic Encyclopdeas also seems to be stuck in a time warp and has an erroneous teaching.
Purgatory (Lat., "purgare", to make clean, to purify) in accordance with Catholic teaching is a place or condition of temporal punishment for those who, departing this life in God's grace, are, not entirely free from venial faults, or have not fully paid the satisfaction due to their transgressions.
Thomas Aquinas also taught erroneously that there was punishment in purgatory. In fact he speaks of it so many times that I can give you only a small selection of his words on the matter from the Summa... Obviously, it was one of the popular heresies of his day!
The below is all from Question 2
Question 2. The Quality of Souls Who Expiate Actual Sin or Its Punishment in Purgatory
The severity of that punishment is not so much a consequence of the degree of sin, as of the disposition of the person punished, because the same sin is more severely punished then than now. Even so a person who has a better temperament is punished more severely by the same sentence than another; and yet the judge acts justly in condemning both for the same crimes to the same punishment.
In Purgatory there will be a twofold pain; one will be the pain of loss, namely the delay of the divine vision, and the pain of sense, namely punishment by corporeal.
It would seem that this punishment is voluntary. For those who are in Purgatory are upright in heart. Now uprightness in heart is to conform one's will to God's, as Augustine says (Serm. i in Ps. 32). Therefore, since it is God's will that they be punished, they will suffer that punishment voluntarily.
Further, every wise man wills that without which he cannot obtain the end he has in view. Now those who are in Purgatory know that they cannot obtain glory, unless they be punished first. Therefore they are punished willingly.
On the contrary, no one asks to be freed from a punishment that he suffers willingly. Now those who are in Purgatory ask to be set free, as appears from many incidents related in the Dialogue of Gregory (iv, 40,65). Therefore they will not undergo that punishment voluntarily.
It is, however, possible that they [the angels] take them to the place of punishment
Since the obligation incurred by guilt is nothing else than the debt of punishment, a person is freed from that obligation by undergoing the punishment which he owed. Accordingly the punishment of Purgatory cleanses from the debt of punishment