The Council of Trent defines Justification as:
"not remission of sins merely, but also the sanctification and renewal of the inward man, through the voluntary reception of the grace, and of the gifts, whereby man of unjust becomes just, and of an enemy a friend, that so he may be an heir according to hope of life everlasting." (Sixth Session, Chapter VII)
The Council of Trent also explained the causes of justification as these:
the final cause indeed is the glory of God and of Jesus Christ, and life everlasting; the efficient cause is a merciful God who washes and sanctifies gratuitously, signing, and anointing with the holy Spirit of promise, who is the pledge of our inheritance;The "great divide" is really over the how the formal cause (justitia Dei) is understood and received. It's worth noting that that the Church teaches that "we are not only reputed" as being just, but are "just, receiving justice within us."
the meritorious cause is His most beloved only-begotten, our Lord Jesus Christ, who, when we were enemies, for the exceeding charity wherewith he loved us, merited Justification for us by His most holy Passion on the wood of the cross, and made satisfaction for us unto God the Father;
the instrumental cause is the sacrament of baptism, which is the sacrament of faith, for without faith no man was ever justified;
the formal cause is the justice of God, not that whereby He Himself is just, but that whereby He makes us just, that, to wit, with which we being endowed by Him, are renewed in the spirit of our mind, and we are not only reputed, but are truly called, and are, just, receiving justice within us, each one according to his own measure, which the Holy Ghost distributes to every one as He wills, and according to each one's proper disposition and co-operation.
Whatever God speaks actually occurs. If God says, "Let there be light," there is light. If he declares "John Doe is just on account of the merits of Christ," then John Doe really is just. The justified are not only clothed in Christ they are renewed and conformed to Christ - even partakers of the divine nature (2 Pet 1:4). Our union with Christ allows us to actually share in His righteousness. This is not an "alien righteousness" but an indwelling righteousness.