'Proselytizing' to me means the aggressive pressure of a religious message, part of a program directed solely towards accumulating members in one's own religious group. This could be Jehovah's Witnesses knocking on the door, being made to sing Christian hymns before being fed at a soup kitchen, or a society making it inconvenient or stricter penalties for not belonging to the majority faith.
Pope Francis, whom all Catholics see as an authority on the subject, says no to this form of witness.
'Evangelization' means living out the Gospel as passionately as we can, always ready to share what we've experienced of Christ. It means demonstrating unconditional love to each other and to all God's children, regardless of creed. The idea of evangelization is to send an authentic message: God loves you, and I love you too. Period. No 'if' in that sentence.
So Catholics rush to treat victims of natural disasters, no matter where they live, and they leave their pamphlets at home. Catholics make use of religious freedom to hold a public way of the Cross, calling society to remember justice. Catholics teach all kinds of students, especially those who nobody else will.
Sometimes we fail at this. Some Jewish children who were left with Catholics in WWII were not returned to their faith. The idea was their salvation had to happen in Catholicism or their souls would perish. The future Pope John Paul II vehemently rejected this thinking and ordered all Catholics to raise Jewish children Jewish.
Vatican II officially taught that God has the power to save all peoples, with or without the sacraments of the church, and that there is truth and value in other religions. This is probably where you could say the Church stopped proselytizing, because it stops being a moral issue to save individuals from their freely chosen faith.
Finally, Catholicism does suffer from being too quiet about what our faith gives us. In ordinary ways, ordinary Catholics have a tough time saying anything about what they believe, and on a global scale, we provide so much care and love, such as to a third of the world's AIDS patients, that no one knows about.