Except that it *actually* *is* AmigaOS, and is a continued development from the OS that shipped with Commodore Amigas. But even if it wasn't, it wouldn't change the fact that legally it is the only OS allowed to be called AmigaOS.
ExecSG is not a continued development and did not exist before the OS4 project began.
Of Intuition, Workbench, and the shell - only Hyperion really knows how much - if any - of the original code was actually used. The fact that much of it was written in 68K assembler really strains credibility that any of it was particularly useful, and Hyperion developers have said as much.