Rainbow is or at least WAS Masonic. I come from a long line of mason/shriners/eastern star . Girls were in rainbow and boys were in Demolay. it had nothing to do with Odd Fellows. I had to get my uncles and my grandmother (Masons and Eastern Star) to sponsor me. It really is part of the Masonic order. I have actually never heard of Job's daughters, maybe there are regional differences and the names are just different??? No idea on that one...
Now, after saying that....I am now Catholic and would never let my daughter join Rainbow...I do remember those meetings as if they were yesterday...it was 35 years ago...