I think the biggest difference between a true Rhode Island red and a production red lies primarily in the eyes of those who stick their noses in the air and look askance at anything that comes from a hatchery.
Production reds are, as others have pointed out, most likely a cross between a New Hampshire red & a Rhode Island red which are very similar in appearance, with the New Hampshire red being a slightly lighter color and somewhat smaller bird. Someone mentioned they've seen red sexlinks sold as PRs, but that has not been my experience. I've only seen red sexlinks sold as red sexlinks, red stars, or cinnamon queens. (I like the name "cinnamon queens" better hehehe... it just sounds prettier.) How chickens are labeled for sale varies greatly from region to region and even from one hatchery or breeder to another.
I don't get into semantics and hair-splitting when it comes to identifying breeds, though. If it's red, lays a brown egg, has a good disposition, and is sold to me as a Rhode Island red, that's what I'm gonna say it is. I think it really matters more if you're planning to show or get into breeding, but if you just want some nice fresh eggs and a bird that's going to be docile and get along well in your flock, you just can't go wrong with a RIR.