There are many Orders! So many ways to serve the Lord ≋♥≋ All Nuns are Brides of Christ but they may (or may not) wear a wedding ring depending on the tradition of the Order.
And some that received a ring during final vows simply don't wear it because of their work.
Nuns and Monks take the traditional three: poverty, chastity and obedience
(Priests do NOT vow poverty) and Orders often have extra vows- for example, Mother Teresa's Missionaries of Charity vow "service to the poorest of the poor"
Consecrated Virgins wear wedding rings but do not receive a habit; they live in the world but are not of the world. Some Religious Orders are discalced (no shoes/possibly sandals) some are vegetarian & some receive Communion under one form only, having taken a vow of temperance.
You did not ask, but Hermetic life is going strong in our modern age also!
I hope this has been helpful.
GOD BLESS EWE