Conurbations:
A conurbation is a region consisting of a number of densely populated cities and their surrounding suburban and urban areas. It is characterized by the merging of multiple cities or towns into one continuous urban area. Conurbations usually occur due to rapid urbanization and population growth, resulting in the expansion of existing cities and the emergence of new settlements.

Metropolitan City:
A metropolitan city refers to a large urban area that serves as the economic, political, and cultural center of a region or country. It typically includes a major city and its surrounding suburbs, towns, and satellite cities. Metropolitan cities are characterized by significant population density, diverse economic activities, advanced infrastructure, and various amenities. They often have a well-developed transportation network and are hubs for commerce, governance, and cultural activities.

Metropolis:
A metropolis is a term used to describe a major city or urban area that is the primary center of economic, political, and cultural activities within a larger region or country. It is typically characterized by its size, influence, and significance. Metropolises are usually densely populated and serve as hubs for commerce, finance, education, research, and innovation. They attract a large number of people from surrounding areas due to job opportunities and a wide range of services and amenities.

Megalopolis:
A megalopolis refers to a vast and highly populated urban region that consists of multiple interconnected metropolitan areas. It is formed when several adjacent metropolitan areas grow and merge together, resulting in a continuous urban sprawl. Megalopolises are typically found in highly industrialized and developed regions, often spanning across multiple cities and states. These areas are characterized by high population density, extensive transportation networks, and significant economic interdependence. Examples include the BosWash megalopolis in the United States and the Taiheiyō Belt in Japan.

Differences:
- Conurbations are regions where multiple cities merge into one continuous urban area, while metropolitan cities refer to large urban areas that include a major city and its surrounding suburbs.
- A metropolis is a major city that serves as the central hub of economic, political, and cultural activities, whereas a megalopolis is a vast urban region formed by the merging of multiple metropolitan areas.
- Conurbations and metropolitan cities are smaller in scale compared to megalopolises, which encompass much larger areas and populations.
- While conurbations can occur through rapid urbanization and population growth, metropolitan cities and megalopolises are usually the result of long-term development and expansion of urban areas.
- Metropolises are often the primary centers of governance and cultural institutions, while megalopolises represent a higher level of urban integration and economic interdependence.

Overall, these terms represent different scales and stages of urban development, with conurbations being the smallest, metropolitan cities being larger and more developed, and megalopolises representing the largest and most interconnected urban regions.