Actually, Abraham Lincoln did not obtain a Declaration of War against the Confederate States of America. Try finding the text of such a declaration of war. You will never find it.
The United States of America never declared war during the Civil War. This was in keeping with its position that the rebel states did not form a new nation, rather they were states in which a rebellion was taking place. Abraham Lincoln issued a Proclamation that an insurrection existed in the states of SC, GA, FL, AL, MS, LA, and TX on 15 Apr 1861 (Messages & Papers of the Presidents, vol. V, p3214). He also proclaimed a blockade of Southern harbors on 19 Apr 1861, and the date of this proclamation was taken by the Supreme Court in several cases to be the official beginning of the insurrection.
In the war against terrorism, a declaration of war is not appropriate when you are fighting what legally amount to saboteurs, filibusters, pirates and terrorists. Wars are declared against sovereign states. These individuals represent no sovereign state.
Congress has passed an authorization to use force against all the organizations linked to the 11 September attack. That is the Constitutional equivalent of a declaration of war when a sovereign nation is not the enemy.
Legally, anyone who attacks the U.S. automatically becomes a belligerant the instant that the attack starts. The U.S. Navy was shooting back at the Japanese on 7 December 1941 although Congress had not yet declared war. Japan clearly defined itself as a belligerent by it's own action. Any foreign group, either known or previously unknown, who attacks or facilitates an attack on the U.S. is likewise an automatic and defined belligerent by it's own action.
In regards to terrorists living within the U.S., Abraham Lincoln has set the historical precedent that the President can declare a certain group of people to be in a state of insurrection against the U.S.
Beautifully done.