Firstly, I accept Beeston's proposal to refer ‘to linguistic data as Minaic, Sabaic, Qatabanic and Hadramitic, leaving Minaean etc. for non-linguistic contexts’ (Beeston, 1987a: 13). His argument (at least with respect to the distinction between the ‘Sabaean’ and the ‘Sabaic’) looks entirely convincing:
The Sabaeans were the inhabitants of the area around Ma'rib. But they shared a common language(no doubt with dialectal varieties) with the peoples of the desert fringes between Ma'rib and Wadial-Jawf, of a considerable part of Wadi al-Jawf itself, and of the high plateaux lying in the angle of those two areas—Arḥab, Qā‘ al-Bawn, Qā‘ Ṣany‘ā’ etc. It is dubious whether these other peoples would have called themselves Sabaeans,1 and it might be preferable therefore to term the language Sabaic rather than Sabaean’ (Beeston, 1979: 115).