production reds are what hatcheries sell in place of RIRs... they do not have the dark mahogany coloring of show birds, but a lighter red color.
What you have is an ISA brown or Red Sex Link... These are chicks bred so that the male chick is white and the female chick is red. They can be sexed at their hatch by color... This makes it easier to sort them. ISA and Red sex link chicks are not "production reds", but are similar in type. ISA and Red Sex Links tend to have white feathering as well as red, just like your hen.
When I said you had a "production" hen, I didn't mean a Production Red, I meant a hybrid breed of hen that is created for increased egg laying production. These newer hybrid breeds do not breed to standard, and are bred solely for increased production.