しゅと首都shuto
1.

A city that serves as the seat of government for a nation, where political leaders and central administrative functions are concentrated.

2.

The primary urban area within a country that is designated as the center for political authority and governance, often housing key government institutions and officials.

Example:

東京は日本の首都です。

しゅとけん首都圏shutoken
1.

A geographical region surrounding Tokyo that encompasses the capital city and its neighboring prefectures, designed for urban planning and population management.

2.

An area that includes Tokyo and its closely connected surrounding regions, formed to balance urban development and maintain a specific living environment.

3.

The area that contains Tokyo and extends to nearby prefectures, characterized by coordinated development efforts to prevent overpopulation and distribute facilities like schools and industries.

4.

A metropolitan zone centered around Tokyo, comprising Tokyo and several adjacent prefectures, aimed at regional planning and infrastructure development.

Example:

首都圏でも燃料が不足している。