I once saw online that there is a Catholic classification or special private ceremony for women who are chaste and do not engage in any form of sex. This is for women who are not nuns or sisters. Is there such a thing?
Nuns (contemplatives) or sisters (active life, e.g., teaching, nursing, etc.) belong to religious orders or congregations. They take vows required by their order, which include the vow of virginity.
A lay person can make a private vow to observe virginity "under the virtue of religion."¹
a vow of perfect chastity by a lay person…could be a public vow only if it were made in the name of the Church and accepted as such by a legitimate ecclesiastical superior.¹
Although "such a public vow was forbidden by the Holy See in 1927,"¹ it is permitted by the 1983 Code of Canon Law canon 604, as it had been at other times in Church history.
- A vow is public if a legitimate superior accepts it in the name of the Church; otherwise, it is private.
- A vow is solemn if the Church has recognized it as such; otherwise, it is simple.
Vows are also either perpetual or temporary. Vows differ from promises in that vows bind under the virtue of religion; viz., to break a vow is a sin against the virtue of religion.
- ch. 5, "The Manner of Dedication," of The Mystery of Love for the Single: A Guide for Those Who Follow the Single Vocation in the World by Fr. Unger. For an explanation of the 1927 denial, see: "Explanations for the 1927 Denial" (PDF pp. 129-33) of the 2019 dissertation by Judith M. Stegman
cf. also Pope Pius XII's encyclical Sacra Virginitas and this informative blog written by a consecrated virgin
Desiring to expand on Geremia's answer, I would like to add the following.
The consecration of a virgin living in the world, which dates back to the earliest years of the Church, fell into disuse for centuries before it was restored after Vatican II.
Worldwide, there are approximately 3,000 consecrated virgins, with an estimated 215 in the United States, according to the U.S. association, which currently has about 100 members. Many consecrated virgins are aged 40-60 and hold a variety of professions, according to Judith Stegman, the association’s president.
Consecrated virginity is not a sacrament because there is no outward sign (unlike marriage, the consecrated virgin’s spouse, Christ, is not visible). The consecration is public and permanent, per the Code of Canon Law. "Through their pledge to follow Christ more closely, virgins are consecrated to God, mystically espoused to Christ and dedicated to the service of the Church" (Canon 604 on the Order of Virgins). "In itself, the state of consecrated life is neither clerical nor lay" (Canon 588), so the women remain in the secular state in the world.
According to the Rite of Consecration to a Life of Virginity, it is "a solemn rite constituting the candidate a sacred person, a surpassing sign of the Church’s love for Christ and an eschatological image of the world to come and the glory of the heavenly Bride of Christ." Thus it is open only to women because they alone can physically image a bride, Stegman explained. - Consecrated Virgins: Witnesses to Christ’s Love for All Souls
The actual Rite of Consecration to a Life of Virginity can be found here: CONSECRATION TO A LIFE OF VIRGINITY FOR WOMEN LIVING IN THE WORLD.