In the study of human settlements, an agglomeration\ is an extended city or town area comprising the built-up area of a central place (usually a municipality) and any suburbs or adjacent satellite towns.
Conurbation is a more specific term for urban clusters where the built-up zones of influence of distinct cities or towns have joined but each continues to act as an independent focus for a substantial part of the area.
A metropolitan area is an extended agglomeration or conurbation including also peripheral areas not themselves necessarily urban in character but closely bound to the urban area by employment or commerce.