A person in Korea under an F1 visa cannot work legally in the country. The F4 visa allows you to live and work in Korea.
The F1 visa must be renewed after one year, and you must leave the country to have a new visa issued. The F4 visa allows you to live and work in Korea indefinitely. It lasts two years but can be renewed without leaving the country.
The F1 visa requires you to have a sponsor inside Korea. The sponsor can be biological family, a native Korean spouse or a native Korean friend who assumes responsibility for your actions in Korea. The F4 visa does not require a sponsor and allows the holder to purchase land, property, housing or open up a business in Korea.
The F1 visa is a Korean family visa issued to people who have a Korean sponsor such as a family member, native Korean spouse or native Korean friend. The F4 visa can only be issued to people of Korean descent residing overseas that immigrated after 1948, overseas Korean nationals, foreign Korean nations, Koreans born overseas with another citizenship and Koreans who have changed their citizenship.