To me, hybrid is the F1. I call red sex links a hybrid, as the results are predictable and stable. But mate those F1s together, and your results are all over the place, so to me at this point you simply have a mixed breed bird. Again, not any official defination, just how my brain works.
I think if a hatchery infuses straight Leghorn blood into a production red strain, the F1 birds aren't necessarily sold to the public, but used as breeding stock to breed back to more red birds to get back to a basic Red type. So you're not going to see the first generation or so...again, just how my brain works and how I'd do it.
I wouldn't call a production red a hybird, as you can breed a male to a female and get stable, predictable results with each parent being the same breed. To me they're a breed, just not an official breed with a standard. Just as many of us can look at a bird and say "That's an Easter egger", even though there's no standard and the EE appearance is more over the board than a production red. Being able to look at a bird and say it's a production red, and knowing if you mate it to another production red, in my mind makes it a breed. SOP folks might like me using the words type or strain instead of breed, but again I'm in my own little head and since there's no official defination of these terms, it works for me!