We also make a vow of poverty. This means that we do not own anything individually. In some orders, it means that the order does not own anything as a corporate body. Secular deacons and preists can own property. They can be millionaires. If your father owns Microsoft and you're his heir, guess what!
If you're a religious and your father owns Microsoft, you don't have the right to inherit. You sign away that right before you make final vows. You must assign your inheritance to someone else outside of the community.
In some communities, you're allowed to own a small number of things that are necessary. In others, you own nothing and you literally have nothing. In my community you own nothing. When we are transferred, the only things that we take with us are habits, breviary, bible, toothbrush, a few clothes and any little trinket that the superior has allowed you to take. You can fit it all in the backseat of a car. Oh, by the way, you don't own the car either. Whaterver you had for your use while at that house stays behind for the next guy.
Probably the biggest difference between a religious and a secular is community. A priest who belongs to a religious order is first and foremost a consecrated man. If he's a Dominican, Franciscan, Jesuit, Carmelite, etc, his first duty is to live according to the charism and vision of his order. Being a priest is a vocation within the vocation. If he's a Dominican and a priest, he lives and works as a Dominican. His priestly duties cannot interfere with his obligations to the Dominican way of life and to his Dominican brothers.
For example, Franciscans have many priests. But we are a brotherhood, a family. If a priest has to give up saying a mass or hearing confessions to pray with his brothers, recreate, eat a meal, do manual labor with them, take care of a sick brother, that's what he has to do. When he goes out to perform priestly ministry, he goes out as a brother to the laity.
Another important part of community living is the fact that not all members of a religious community are priests. But they are all equal. This is a concept that is foreign to secular or diocesan priests. They live with other priests. Their boss is a pastor. In a religious community you may be the only priest in the house and your boss may be an accountant or a teacher. But that boss is as much a religious as you are and has authority over you, even though you're a priest. Those brothers who are not priests are your equals, not your subordinates. When making plans, meeting in chapter, discussing goals for the community, you're subordinate to them and they to you. Among the secular clergy their is a "pecking order" that we don't have in religious life, from bottom to top: deacon, priest and bishop. In religious life, we have some religious who are cardinals. When they walk in the door, guess what? They get to do dishes like everyone else.
To give you an example of the difference, I'll share the story of St. Bonaventure. Bonnie was a Franciscan. He was ordained a priest and later elected the superior general. While he was the superior general he was ordained a bishop. To comply with his obligations to the order, he had to run the order and a diocese at the same time. He had been elected by his brothers. Obedience requierd that he fulfill his duties. One day, while washing dishes, a messenger arrived from Rome with his red hat. He had been elevated to Cardinal. Remember, at this point he is the superior general and a bishop; but he's washing dishes. Why? He was not the superior of the house, only the superior of the order. The superior of the house had assigned him to kitchen duties. Interestingly, the superior of the house was not ordained. Bonaventure, being a saint, told the papal emissary to hang the red hat on the branch of a tree, because if he stopped washing dishes to read the pope's letter he would be in big trouble with the superior. He had to finish his work first, before he could take care of the business of the Church.
Today we have someone like Cardinal Sean O'Malley who is a friar. He still has to tow the Franciscan line, even while he governs the Archdiocese of Boston. Cardinal Pell of Australia is a Dominican. He too must tow the Dominican line. The work of the Church their life as religious can never be in conflict. If they are, the Church herself says that they must first attend to thier religious life, then to other things. Religious life also allows them to attend to the work of the Church, within reason. That's going to vary from one order to another. Secular and diocesan clerics do not have these mandates.
I hope this helps.
Br. JR, OSF :)