Someone who works in said US defense industry here
Neither defense nor war really apply to what we do, but between the two defense is the more apt description. The DoD largely uses a strategy of deterrence, where the technology we develop and training done for the "war fighter" is just public and visible enough that no other major country wants to take the risk of going into full open conflict with the US. Since most efforts go into deterrence, and deterrence is a defense strategy, it does become the more appropriate word.
Sure the US loves its proxy wars, but those don't throw the entire nation into wartime. Plus, in a round about way proxy wars help with the deterrence since we get an outlet for the decades old stock piles of arms that we no longer want and want to replace with the new stuff. If our waste products are being useful in places like Ukraine, it helps build up an idea of what it is we keep for ourselves, again building up a deterrence of openly and directly attacking the US
What I was referencing by proxy war was Ukraine and what Israel was supposed to be. The US sends arms to another nation with the intention that the other nation, who is already in conflict (or just happens to be through dubious and convenient circumstances) will take those arms and give political adversaries a bloody nose or serve as enough of a distraction that they won't come after the US and keeps the US from putting boots on the ground. Is working out quite well for us in Ukraine, Israel was supposed to distract the middle east but turns out that when you hand a genocidal maniac a bunch of weapons, he's gonna do maniacal genocidal things with them. Who could have possibly guessed