My understanding is that the FR is a red bird, while the Dixie Rainbow, also known as a Pioneer has sex linking in it's breeding, at least the ones I had did. The females were a light brown/red with a bit of variation in the coloring. The males were a much lighter color and were all barred. IIRC, the females had willow colored legs, and the males had yellow legs.
You are correct in that each hatchery will have their own "recipe" or breeding program for the birds they offer. The ones I describe came from Murray McMurray 3 - 4 years ago.