correction: as far as I know 'Arab' relates to the Arabic speaking peoples and their culture and art and architecture etc, both historically and contemporarily. This may span a large area including Spain and North and Atlantic Africa and the Levant and the Arabian peninsula etc. and many nations and many races. You can refer to Arab architecture in Sicily, or Arab speakers in Chad or Tanzania
Arabian on the other hands relates to the geographical area of Arabia itself, either the Semitic race of Arabia specifically or something from the original home of Arabic, which is the Arabian peninsula. Old Arabian poetry for instance specifically comes from the peninsula (not poetry in Arabic from Egypt for instance)
In Arabic that distinction is not very clear - for what it is worth (some think it should be made, others think it shouldnt).
The course seems to want to translate the word only as 'Arab'...