Third orders are associations of non-clerics set up by religious orders. They are divided into two categories, secular and regular.
Third order secular members are affiliated with, but do not belong by public vows to, particular religious orders. They are secular in the sense of being actively engaged in the secular world. They don't live in religious communities, yet they strive to live according to the principles of the religious order with which they are affiliated.
Third order regular members belong to religious communities, which means they profess public vows and live in community, but aren't clergy--that is, they aren't ordained. They are called regular because they follow a specific rule of life--their lives are, so to speak, regulated.