The term "Arabian countries" most precisely refers to the sovereign states on the Arabian Peninsula:
Includes Levant (Jordan, Lebanon, Syria, Palestine), North Africa (Egypt, Libya, Tunisia, Algeria, Morocco, Mauritania, Sudan), plus Comoros, Djibouti, Somalia. United by Arabic language & Arab League membership.
Gulf Cooperation Council (6): Saudi Arabia, UAE, Qatar, Kuwait, Bahrain, Oman. Economic/military alliance.
"Arabian" = geographic (peninsula). "Arab" = linguistic/cultural. Iraq is both; Egypt is Arab but not Arabian.