The war on terror lacks an easily identifiable or locatable enemy, unlike World Wars I and II and Korea. Identifying the enemy was somewhat difficult in Vietnam. It was not difficult at all in the first Gulf war, nor was it especially difficult (at least at first) during the invasion of Iraq. The war on terror is especially challenging because terrorists could be anywhere, including within the U. S. itself.
I wonder if you are referring to wars in the 20th century, given that the US has not been involved in any wars in the 21st that have not been connected to the war on terror. If so, the major difference is that the war on terror is in no way a traditional war with military objectives. In addition, it is not a war that really even has one country or area as a battlefield. In that way, it is more like the Cold War in that it is being conducted in many different ways and in many different places.
The war on terror does include some things that look more like other wars. Afghanistan and Iraq resemble the Vietnam War in some ways. However, much more of the war on terror consists of intelligence work as American agencies look for individual terrorists and try to disrupt the actions of terrorist networks. This looks much more like the Cold War competition between communist and Western spy agencies.
In these ways, the war on terror is less of a regular war like WWII and more of a seemingly unending conflict like the Cold War.