:salam: Bro :)
Jihad as you have mentioned is struggling for the sake of Allah Most High. There are 2 main aspects:
1) Tassawuf which basically means Tazkiyah al-nafs. This would be what you mentioned about struggling to improve oneself; inner equilibrium. A Sufi is one who uses a Tariqa and Silsilla to do this.
2) To attain external equilibrium one uses Shariah. This is not just about improving oneself but society and helping the people around you be they Muslims or Non-Muslims. It's also a duty on Muslims to spread the message.
Do we need to do Jihad on the West to spread the message? No because they are letting us preach... although there are various hurdles.
There are people with power that are causing corruption on earth due to their greed and it's affecting everyone. ISIS/Daesh should be seen as nothing but another foreign occupier in Muslim land and it is undoubtedly a false flag operation. Thanks to them many have declared open season in Syria.
"And when it is said to them, "Do not cause corruption on the earth," they say, "We are but reformers."
^ Sounds like foreign policy to me
But Physical Jihad in the way of Allah Most High is not for oneself (fame), supremacy, worldly gains and other materialistic reasons; but it is done in order to restore the balance when it is transgressed. it was Mohammad :saws: who encouraged a pluralistic Society. And when the limits where transgressed he applied Sharia.
Regarding what Syed Habib Ali Jifri said; it reminded me that even when we fight physically we are doing it not for our own pleasure and had there been more amicable ways to resolve it we would. For example Salahuddin Ayyubi (Saladin) is noted in the books of history to have given medical help to his opponent Richard the Lion-Heart of England, who was seriously ill during the Crusades. He sent his own doctor and personally supervised Richard's treatment until he became well. Here is more on that war:
The nature of a Muslim in physical battle is not one born out of hatred for his enemy but for in order to serve others for the sake of Allah Most High. So much so that this chivalrous nature was recognized by the crusaders; they held Muslims in high esteem even though they were conquered by them. I can give many more examples but the sad fact is there are some Muslims who do not understand more about Islam than the crusaders these days.