Yes, she's a "Red Star" which means she's a red sex-link. Hatcheries come up with all sorts of names for whatever flavor of sex-link they may have. If she was commercially bred she is likely going to be a good layer. If she's a backyard sex-link she may or may not be.
"Production Red" on the other hand can mean just about anything. It does not have a widely accepted definition. At various swaps and sales I've been too I've seen it applied to sex-links, Rhode Island Reds, New Hampshires, and red hens of unknown provenance. Basically you have to ask the breeder what they mean when they say a bird is a "Production Red" and if the person selling them isn't the breeder then even they may not know if it's not an obvious sex-link.