The judges are picked by the executive but confirmed by the legislative.

Executive is president and staff, legislative are the house and Senate. All are elected. Executive nominates judges and Congress approves or dicks around and holds the seat hostage for a year+ because one party is gaming the system a certain way to the detriment of the country (less judges, longer court lines for everything including immigration which is one reason it's such a clusterfuck). Supreme Court are just the nine most powerful judges of the ultimate court. Since we have multiple levels of judges for various reasons.

The executive branch includes the president (who is elected by the whole country) and their staff, as well as the various departments and agencies such as the FBI, USDA, NASA, etc, which are staffed by unelected government employees.

The legislative branch (Congress) consists of representatives elected by the people of each state.

The judicidal branch is the courts, and the Supreme Court is the highest court. Its 9 justices are nominated by the president and confirmed by a vote in Congress, and serve for life.

Executive and legislative are both in the elected government (except the secretaries, staff, etc.).

The president appoints SC judges.