The Catalogue of Life/October 2015 shows Aloe barbadensis as a synonym for Aloe vera:
Aloe barbadensis Mill. Species synonym for Aloe vera (L.) Burm.f.
Aloe barbadensis var. chinensis Haw. Infraspecific taxon synonym for Aloe vera (L.) Burm.f.
Aloe perfoliata var. barbadensis (Mill.) Aiton Infraspecific taxon synonym for Aloe vera (L.) Burm.f.