Fred's Hens :
A Rhode Island Red is a rare breed of super dark, brick bodied birds. We have a Heritage RIR thread here. Read a bit about it.
A heritage New Hampshire is also somewhat rare. These were established as a separate breed a century ago.
Now, what you are seeing at the hatcheries are New Hampshire (Red) and the word Red being wrongly added. It is kind of a New Hampshire, but no longer pure. The hatcheries sell RIRs too, but they also are a far cry from the heritage strains. Production Reds are merely Red birds from a conglomerate of blood lines that lay very well.
If any of this matters to you, buy from a true breeder. If it doesn't matter so much, then just get what you want and be happy.
x2 - Very well said.
Also to add - Hatchery New Hampshires are usually very reminiscent to Production type Rhode Island Reds, but with a more orange color and often more fluff at the thigh.
True New Hampshires are slightly reminiscent to true Rhode Island Reds, but with some subtle differences. One of course is a bright almost burnt orange color and very noticeable black tails as well as black tickling in the neck.
Photo and Hen from
Kathyinmo
Production type Rhode Island Reds are usually a dull red to orange color, with a skinny body and very thin, pinched, or ratty looking tail, most often sticking up at an angle above 40 degrees.