I think the main difference is color. Hatcheries breed birds more for egg production than breed standard so RIRs that come from a hatchery tend to be from a lighter colored, but more prolific egg-laying strain.
Production reds are autosexing Rhode Island cross (male Rhode Island Red x female Rhode Island white mutation). Hatching female chicks is brown and male chicks is white. Brown egg layers lay 300-320 eggs/year with wight 63-64 gr and Rhode Island Red lay 220-240/58 gr. Production reds are much lighter.
I think you're thinking of red sex-links dr_lukanov.
Production reds are bred for egg production. They have lost the "brick" shape that a true RIR has. They range from a "triangle" shape to a square shape. A true RIR will look like a brick with the edges shaved off. A production red is a lighter color and can range from a yellow-ish color to a dark red. A true RIR will be so dark they are almost black.