Secular—or better, diocesan—priests are priests who are ordained for a particular diocese and who serve ordinarily in parishes. This is their main work, although some are engaged in other ministries as well. At their ordination as deacons they incardinate (affiliate) with a particular diocese or archdiocese. At this time they make a promise to obey their bishop and, in the Western Church, to remain celibate.
Religious priests are not necessarily more spiritual than diocesan priests. The word refers in this case to the form of life these priests live. All men and women who make public vows in a religious order are called religious. It means that by their vows of poverty, celibate chastity, and obedience, their lives are oriented in a special way to the virtue of religion so that all they do becomes a continual act of the worship of God.
This is true of all religious, sisters and brothers as well as priests. Ordinarily they live and pray in community. Many of them wear a religious habit. Often they are engaged in a specialized form of ministry.