Actually, An1OrthodoxChristian is correct. Even before the Great Schism, these terms were used and at the Eccumenical councils the terms Sacred Mysteries and Sacraments were equivocated. The terms actually come from the same word, it is just that the Eastern Churches preserved the original Greek terms and the Roman Churches came to the word through Latin. In Latin, ‘Sacramentum’ literally means ‘Mystery’.
As to the Confession being valid and licit, the Catholic Church and the Greek Orthodox Church lifted the mutual excommunications between them in 1965. Since then, both Churches consider the ordinations of the other’s bishops, priests, and deacons valid; the Sacraments (Sacred Mysteries) of the other valid and licit as pertaining to their own rite and tradition; and the faithful members of the Churches validly able to receive the sacraments of the other Church in times of need when there is no ability to receive them in their own Church.
I am not commenting on the Catholic School topic. I’m staying out of that discussion.