So, if Iraq invades the US but does not declare war, it's not a war?
In the US Constitution, it is quite clearly stated that only the Congress has the authority to declare war by vote. Therefore, if the Congress hasn't voted for war, no war is declared. If its a police state where one man determines policy, he can issue a declaration of war himself. So, if Saddam Hussein said "I declare war on the United States" and then invaded the US, then it would be war. If Saddam Hussein does not say he declares war, but just moves his troops into US territory and start shooting people, then it would be an invasion, but not technically a war. However, in previous cases, the US would typically declare war for the "unprovoked" attack.
President Polk tried to use this as justification for the US-Mexican war back in the 1840s, where a Mexican force launched an "unprovoked" (it was
really provoked) attack against US forces on "US" soil (again, was in dispute). Then, Congress declared war on Mexico. Or, the official declaration of hostilities for WW2 did not come until after Pearl Harbor.
Now, civil wars typically are not called such until afterwards, and only if the rebels are successful. The declaration of war occurs between two sovereign nations, and the official government typically does not recognize the rebel government until
after the rebels are successful. Note there was never an official declaration of war on the rebels in the South during 1861-1865 by the US Congress, because that would imply the Southern government was "legitimate".
What r_rolo posted is technically correct.