Spider Lily - two types - difference?

[Dinu]

I have these Spider Lilies. Their flowers are slightly different. The collage below is self explanatory. Can someone identify the different names they may have? All these years, I had not thought of seeking this information and I myself wonder why!!

 

[IcyBC]

They are beautiful but I can't identify them. I saw the one on the left at a Conservatory around here before, but the one on the right is new to me. Do you have them in your garden?