The Elements of the Crime
There are four elements to the crime of terrorism. Each of the following criterion below must be present for the action to be classified as terrorism.
Violence or the threat of violence
Violence against an innocent third party
Violence for the purpose of creating an atmosphere or terror
Violence which may be exploited for political purposes
The attacks on the Twin Towers and the Pentagon, and the unsuccessful attempt that ended in a field near Shanksville, PA are examples of attacks using both terrorism and standard battle tactics.
In this case in which three coordinated attacks were executed, the classification of the tactics used is:
Operation Target - Classification
Twin Towers, NYC-Terrorism
Pentagon, WASHDC-Conventional Warfare
White House, WASHDC-Conventional Warfare (Unsuccessful)
For a tactic to be "terrorism," it must meet all four of the criteria above.
The attack on the Twin Towers in New York City was terrorism because it met all four of the criteria.
The attacks on the Pentagon and the White House, albeit the latter was unsuccessful, are not terrorism because they do not satisfy the second criteria; that is, they were not against an innocent third party.
The organization conducting the attack, Al-Qaeda, had publicly declared war upon the United States. Therefore, an attack against an enemy military or governmental command-and-control is a legitimate target, even if civilian employees are harmed. This includes action against military members when they are on leave or outside the "field of battle."
War was legitimately declared. If the government of the United States chose to ignore the declaration, it is not the fault of Al-Qaeda.
However, because the Twin Towers attack specifically targeted non-military, non-governmental civilians that attack was terrorism.
Reference: John Rodger Schoonover, Commander, United States Navy Reserve (Retired)