Jihad can be described as "holy war", or more precisely it means the legal effort to expand the territories ruled by Muslims at the expense of territories ruled by non-Muslims. The purpose of jihad is not directly to spread the Islamic faith but to extend sovereign Muslim power. Jihad thus has the eventual goal of achieving Muslim dominion over the entire globe. Jihad ha two main different meanings. The first is that Muslims who interpret their faith differently are infidels and therefore targets of jihad. The second meaning rejects the legal definition of jihad as armed conflict and tells Muslims to withdraw from the worldly concerns to achieve spiritual depth. Jihad in the sense of territorial expansion has always been a central aspect of Muslim life. That's how Muslims came to rule much of the Arabian Peninsula by the time of the Prophet Muhammad's death in 632. Jihad is often described as the fifth pillar of Islam. (Internet Book)
"An appeal to the Islamic tradition of defensive jihad by which every Muslim is obligated, as an individual duty, to take up arms against invaders. It lays out the justification not only for the attacks of September 11 but also for other terrorist attacks linked to bin Laden’s al–Qaeda group, notably, the bombings of the two American embassies in East Africa and of the U.S.S. Cole. It also provides a warrant for future attacks by every Muslim who can do it in any country in which it is possible to do it for a continuing war by terrorist and other means by Muslims against Americans and their allies."
Just War can be described as it deals with the justification of how and why wars are fought. The justification can be either theoretical or historical. The theoretical aspect is concerned with ethically justifying war and the forms that warfare may or may not take. The historical aspect, deals with the historical body of rules or agreements that have applied in various wars across the ages. There are sveral principles of Just War. One of them is that a just war can only be waged as a last resort. All non-violent options must be exhausted before the use of force can be justified. It continues on to say that a war is just only if it is waged by a legitimate authority. Even just causes cannot be served by actions taken by individuals or groups who do not constitute an authority sanctioned by whatever the society and outsiders to the society deem legitimate. A just war can only be fought to redress a wrong suffered. Further, a just war can only be fought with right intentions: the only permissible objective of a just war is to redress the injury. A war can only be just if it is fought with a reasonable chance of success. The ultimate goal of a just war is to re-establish peace. More specifically, the peace established after the war must be preferable to the peace that would have prevailed if the war had not been fought. The violence used in the war must be proportional to the injury suffered. States are prohibited from using force not necessary to attain the limited objective of addressing the injury suffered. The weapons used in war must discriminate between combatants and non-combatants. Civilians are never permissible targets of war, and every effort must be taken to avoid killing civilians. These are the main principles of Just War. Just War can also be described as a war that needs to be morrally justified. (Internet Book)
While the idea of just war is deeply rooted in Western culture, it is perhaps more strongly rooted today in international law, in American military doctrine and practice, and even in political culture. Though the just war tradition has important Christian roots, it differs from the Islamic juristic tradition in that it can be employed without explicitly religious premises. Similarly, in Western political thought and theology more generally, the nature of the political community, the role of government, and the use of armed force are conceived in secular rather than religious terms. All these features differentiate just war tradition from the juristic tradition of jihad by the authority of the caliph.
In conclusion, Just War and Jihad are very simular, however, just war in a way is an effect of the original idea of jihad.