What [exactly] is Military Jihad?

Let's consider the following two sentences:

1. He looked at her greedily
2. He looked at her hungrily

Whilst statement 1 is grammatically correct, its bad use of English. Sentence 2 would normally be used.

Now based on my Islamic Model, one would normally use 'Jihad' in the Military context to 'struggle/strive to achieve excellence as a Military Officer in a Military Academy'. On the battlefield:

1. Using 'Jihad' implies 'a struggle' to achieve victory
2. Using 'Harb' implies 'fighting ferociously' to achieve victory

One could use 'Jihad' in this context but it would be 'bad use of Arabic' - instead 'Harb' would be used. Bearing in mind demented Arabs keep screaming 'Jihad Jihad' instead of 'Harb, Harb', [forgive me if I'm wrong but] I am left somewhat bemused at the [apparent] poor use of their own language [by the Arabs]!