People in law enforcement will sometimes describe Hezbollah as less of a "terrorist" organization than a very well-armed and very well-trained organized crime family . . . sort of like the Sopranos with extensive training in explosives and guerilla warfare.
Al-Qa'ida is a great exception among major terrorist groups. They don't have any one goal, per se. They're not looking to seize territory, or repel an invader. They're religious fanatics for it's own sake. As opposed to Hizbullah or they Jaysh e-Muhammed, there's no strip of land that, once captured, they will call victory. While that makes AQ seem completely insane, it also makes most extremist groups easier to fathom.
They do have goals. Those goals need resources, and they have a political context. Hizbullah has no need to attack America to further their goals. All it would do is deny themselves funding, and make America an even tighter ally of Israel.