As proper nouns the difference between izzy and aurora

is that izzy is {{given name|female|diminutive=Isabel}}, Isobel, or Elizabeth while Aurora is roman goddess of the dawn; equivalent of the Greek Eos. Sister of Luna and Sol.

As a noun aurora is

an atmospheric phenomenon created by charged particles from the sun striking the upper atmosphere, creating coloured lights in the sky. It is usually named australis or borealis based on whether it is in the southern or northern hemispheres respectively.