Can you provide a reference for this? I have never known a distinction between Arab and Arabian as adjectives. None of the dictionaries I have in my collection support this distinction.
The Shorter Oxford Dictionary gives Arab as (n) "a native of Arabia"; adj "of or pertaining to Arabia or the Arabs", and Arabian as (adj) "belonging to Arabia".
The Heinemann Australian Dictionary considers Arab to be the noun and gives Arabian as an adjective form of Arab, which is how I have always used both words.
Most of my dictionaries are fairly old, but a short search online found: "As adjectives, the New Oxford American Dictionary defines Arabic a related to the language or the literature, while Arab is the more generic term (“of or relating to Arabia and the people of Arabia”) and Arabian is a historical variant of Arab."
So for the purposes of this question, someone who translated malikah 3arabiyyah as An Arabian Queen should not be marked down as not understanding the Arabic text. This would seem to me to be a perfectly correct translation.
'Arabian' used to be much more widely-used than it is now - my variety of English (British) uses it exclusively about horses or the collection of stories 'Arabian Nights'. It sounds odd applied to a person: https://brians.wsu.edu/2016/05/17/arab-arabic-arabian/