A more thorough explanation:

An independent state is a political community that has its own government and is not subject to the authority of a larger entity. It has complete control over its internal affairs and is recognized as a sovereign state by other countries.

For example, the United States is an independent state because it has its own government and is not controlled by any other country. It has the power to make its own laws, conduct foreign relations, and defend its borders.

On the other hand, a part-sovereign state is a political community in which some of the powers of external sovereignty are exercised by the home government, and some are controlled by another political body. An example of this is Puerto Rico, which is a territory of the United States. While it has its own government, it is not fully independent because it is subject to the authority of the United States government in certain areas.

These examples illustrate the concept of an independent state and how it differs from a part-sovereign state. An independent state has complete control over its internal and external affairs, while a part-sovereign state has some limitations on its external sovereignty.