We discussed this sometime back. An Archbishop heads an Archdiocese. A Metropolitan heads a Province.
Generally, all metropolitans are archbishops, but not all archbishops are metropolitans. For example, the archbishop of the Galveston-Houston Archdiocese is also the metropolitan of the Galveston-Houston Province (which basically covers East and South Texas). On the other hand, the Archbishop of Winnipeg, Manitoba, Canada) is not a Metropolitan. There is no Winnipeg Province.
In short, there are two entirely different entities which a Metropolitan Archbishop heads. He is bishop of his own archdiocese and he is the metropolitan of a province. For example, a few weeks ago Cardinal diNardo, the metropolitan archbishop of Galveston-Houston, celebrated Mass at the Basilica of Nuestra Senora de San Juan del Valle, which is located in the Diocese of Brownsville (one of suffragans in the Galveston-Houston Province). When celebrating that Mass, the Cardinal was acting as a Metropolitan. He was vested with his pallium–the sign of metropolitical authority. As Metropolitan, he has faculties to celebrate Mass anywhere in the Province and wear the pallium anywhere in the Province and he doesn’t need to ask permission of the local ordinary to say Mass. However, if Archbishop Gomez of San Antonio were to say Mass at the same basilica, he would need permission from Bishop Pena of Brownsville. Further, he couldn’t wear the pallium (as he can only wear it in his province–San Antonio).
There are also titular archbishops. They are appointed to head a suppressed or a diocese that has become extinct. Then they are assigned to other duties in the curia or in the papal diplomatic service.
Finally, there are archbishops who have received the personal title of archbishop. These types of archbishops are archbishops in name only.