This spider Lily was at the Eden Project so I can't take credo for it I'm afraid. With regards to the scientific name it was what was printed on the card beneath the plant. Researching both names gives you a spider Lily so not sure which is correct.
One of my Aussie friends @brightcolours found some info that appears to suggest as recently as 1990 this particular genus of lily was segregated from the Ismene group. I love the flower -- whatever group it belongs to !!