曖昧(あいまい) Vague. Can be intentional, as in an “arty” novel with an ambiguous ending, say, or a girl who gives vague answers whenever you ask her out. “Wanna go to a movie?” “That sounds nice. Let’s do it sometime.” When?” “Sometime.” But 曖昧 can also be unintentional, like a bad public speaker who is vague just because they are not articulate.
らわしい(まぎらわしい) Ambiguous, but unlike the related term 曖昧、紛らわしい has the nuance of confusing. Like you’re not sure who to believe:both interpretations seem equally correct. Is the picture of bigfoot real? It’s so blurry! Is the painting a forgery? The results of the test are ambiguous!
(ばくぜん) Vague like an old memory. I only have a vague sense what the new Matthew Barney is about. Unlike related terms 紛らわしい、or 曖昧、 漠然 emphasizes the speaker’s own sense of confusion – it doesn’t refer to the confusion of the listener.