Here is a quote by the user Della:
Benifits: The difference is that lay order members make promises of obedience to do the things the order prescribes for them and obedience to their superiors. Also, one receives all the spiritual benefits of the order, their prayers, etc. There are also confraternities lay people can join that do not require making such promises, but which are still under the guidance and authority of the order.
Here is a quote by the user Dorothy:
Chaste: Chastity according to one’s state in life is not necessarily celibacy. Third Orders are for the laity, both married and single.
For a married person it means that he/she is faithful to their spouse, and obeys all the moral directives of the Church.
As far as vows of the third order of Carmelite I do believe you make a promise rather than vow. i am not positive but I think that means you promise obedience. I am guessing if you feel devoted to the same charism and devotions as the Carmelite (aside bieng a laymen) then this wont be a problem. So case in bieng I do not think you have a Superior watching over you except for the holy trinity? I do know that you have to attend meetings and I believe there is a few steps to take as well. Once you are in a third order there is no removing yourself or changing from one Order such as the Carmelites to another as lets say the franciscan. Its for life from what I take. Even if you move and there is no other Carmelite Community there it is encouraged for you to start one.
I hope that information helps. I believe I understand now how this works now. If I am wrong I hope I am lucky to be corrected.