The greater Jihad/ lesser Jihad thing is pulled from a Hadith. That is, it is not part of the Koran itself, and is not accepted by all Muslims. Different groups of Muslims accept different sets of Hadiths, and it is also accepted that a certain percentage of Hadiths are incorrect *. Naturally this ones appeals to Islamic mystics. But there are other Hadiths that hold the exact opposite, that there is no act greater then military Jihad.

Jay

* Some Arab Islamic scholars have gone so far as to say that all Hadiths are forged.