1) Terrorists conduct acts of violence against anyone, while an insurgent is primarily a prior regime's holdovers trying to topple the new rule of the land to regain power. For years following the "end" of WWII, insurgents in both Germany and Japan fought against the new governments but to no avail.
What? So fighting a foreign invader makes one an 'insurgent'? What on earth was wrong with the simple term Resistance?
You must have been an awful English teacher if you don't know what "insurgent" means - which is exactly the context in which MODU uses it.
I assure you that the term 'insurgent' will never come up in teaching English to a bunch of Asian kids.
It is, however, of obvious meaning to anyone who understands the common roots of the English word. In any case, before chastising someone for word use, Google it next time.