The following information was retrieved from the website below.
Editorial Note contained in Meaning of Flag Draped Coffin From Chuck Ross.
Please take time to read the following. It should clear up a lot of misconceptions by a lot of people, and will hopefully help people to avoid using the wrong terminology regarding military funerals.
Today, the national salute of 21 guns is fired in honor of a national flag, the soverign or chief of state of a foreign nation, a member of a reigning royal family, and the President, ex-President, and President-elect of the United States. It is also fired at noon of the day of the funeral of a President, ex-President, or President-elect, on Washington's Birthday, Presidents Day, and the Fourth of July.
On Memorial Day, a salute of 21 guns is fired at noon while the flag is flown at half mast. Fifty guns are also fired on all military installations equipped to do so at the close of the day of the funeral of a President, ex-President, or President-elect.
Gun salutes are also rendered to other military and civilian leaders of this and other nations. The number of guns is based on their protocol rank. These salutes are always in odd numbers. For example, the Vice President of the United States, Secretary Defense, and Secretaries of the Army, Air Force, and Navy all rate 19 guns.
The highest-ranking generals in the services (Commadant of the Marine Corps, Chief of Naval Operations, and the Army and Air Force Chief of Staffs) all rate 17 guns. Other 4-star generals and admirals rate 17 guns. Three-stars rate 15, two-stars rate 13, and one-stars rate 11.
At military funerals, one often sees three volleys of shots fired in honor of the deceased veteran. This is often mistaken by the laymen as a 21-gun salute, although it is entirely different (in the military, a "gun" is a large-calibered weapon. The three volleys are fired from "rifles," not "guns." Therefore, the three volleys isn't any kind of "gun salute," at all).
Anyone who is entitled to a military funeral (generally anyone who dies on active duty, honorably discharged veterans, and military retirees) are [entitled] to the three rifle volleys, subject to availability of honor guard teams.
As I said, this is not a 21-gun salute, nor any other type of "gun salute." They are simply three rifle volleys fired. The firing team can consist of any number, but one usually sees a team of eight, with a noncommissioned officer in charge of the firing detail. Whether the team consists of three or eight, or ten, each member fires three times (three volleys).
The three volleys comes from an old battlefield custom. The two warring sides would cease hostilities to clear their dead from the battlefield, and the firing of three volleys meant that the dead had been properly cared for and the side was ready to resume the battle.
The flag detail often slips three shell-casings into the folded flag before presenting the flag to the family. Each casing represents one volley.
Much of the above information compiled from the Naval Historical Society and the Army Center of Military History.