There is not an "official" definition, but some specifications are generally recognized as appropriate for Aerospace and some for commercial/industrial. For instance, Federal specification QQ-A-250/11 for 6061-T6 alloy aluminum plate/sheet was recently cancelled, and steered users to specification AMS4027 published by SAE (Society for Automotive Engineers) for aerospace applications, and to American Society for Testing and Materials (ASTM) specification B209 for non-aerospace applications. They are very similar, but the AMS specification has higher quality and inspection requirements.
I also laugh when I see a product advertised as "aircraft grade" because it is probably just a sales gimmick.
By the way, aluminum is quite often used as a pure metal. Aluminum alloy 1100 is essentially pure aluminum, and has many uses when higher strength is not needed. 6061-T6 is a medium strength alloy, about 3 times stronger than pure aluminum (Fty=35ksi). This is just about equal to the Fty=36ksi strength of ASTM A36 structural steel used for I-beams in buildings. 2024-T3 and 7050-T7 are two very high strength alloys about twice as strong as 6061-T6.