...but I think it matters a lot more than you might think.
It matters what you call things. The War Department had a certain duty. It limited it's activity to a far greater degree than the Defense Department. Part of the reason why you'd call it a Defense Department, is because if you object to defense spending, you're objecting to a notion that is universally viewed as a positive. Therefore, you can get away with doing more shit.
We think in language, Snow. Change the language, and you change the way people think. So, for instance, you can use our military to invade and overthrow a tiny and insignifant nation like Panama, killing 2,000 people, and that's not viewed as an open act of aggression or a war crime because the DEFENSE Department did it.