Is a nun who makes her final profession of vows receiving any kind of sacrament by doing so? Is this the equivalent of holy orders? I understand that such nuns, along with brothers and monks, are therefore members of the clergy, just like priests, except that they aren’t ordained.
Your understanding contains some misunderstandings. Let’s see if we can straighten them out quickly. By making a formal, public profession of solemn vows (the evangelical counsels of poverty, chastity, and obedience) a nun promises to live as a consecrated religious for the rest of her life. This taking of vows is not holy orders, which is the reception of the priesthood. Although they live consecrated lives, nuns (or “sisters “), brothers, and those monks who are not ordained as priests (some monks receive ordination, many don’t) are all lay people. They are not members of the clergy, and it is not correct for us or for them to refer to them as clergy.