Well, Jace definitely does think that any US military achievement is the work of the Marines, and thinks that the Marines are a "special" part of the Army, but he does know that the Navy and Air Force are separate branches (I imagine he neither knows about nor recognizes the Coast Guard). The worst thing about his ignorance in this respect (and others lol) is that it's wilful: he's been told hundreds of times - whether by trolls underlining the point by including the word "fucking" every other word, or by very polite observers recommending he check his facts - and he still stands by his position. The fact that any serving member of the Armed Forces would laugh in his face if he told them he was a veteran and would tear him a new asshole for being a liar goes to show that he has never even talked to a recruiter or asked a veteran about his experiences.
But none of that matters, because Jace is an expert.