Short answers, pulled from the story.
The United States Special Operations Command (USSOCOM) oversees all active and reserve special operations forces across the Army, Marine Corps, Navy, and Air Force. It is the umbrella command under which every designated SOF unit is assigned.
The Joint Special Operations Command (JSOC) is a three-star command that includes the 1st Special Forces Operational Detachment-Delta, Naval Special Warfare Development Group, the 24th Special Tactics Squadron, and supporting elements such as the Joint Communications Unit and Intelligence Support Activity.
The Naval Special Warfare Command organizes SEAL teams into four groups. Group ONE includes SEAL Teams 1, 3, 5, and 7. Group TWO includes SEAL Teams 2, 4, 8, and 10. Group ELEVEN holds Navy Reserve SEAL Teams 17 and 18.
The Naval Special Warfare Center is located in Coronado, California. It houses both a Basic Training Command and an Advanced Training Command.
In the Army, designated SOF career fields include Special Forces, Rangers, Psychological Operations, and Civil Affairs soldiers, but only those in active duty units under USASOC. Reserve and National Guard psyops and civil affairs units are classified as conventional forces, not SOF.
Training is spread across numerous locations, including the John F. Kennedy Special Warfare Center and School at Fort Bragg, the Naval Special Warfare Center in Coronado, the Marine Raider Training Center at Camp Lejeune, and an international facility, the International Special Training Center, in Pfullendorf, Germany.