What is the difference between Prime Rib and a Standing Rib Roast?
I just happened across this older question and found the answers provided, including the information in the link to wikipedia to be incorrect.

All Prime Ribs are Standing Rib Roasts, not all Standing Rib Roasts are Prime Rib.


[see edit below] A "Prime Rib" is a standing rib roast, from a beef that has
achieved a USDA Grade of "Prime".
Bone-In or Bone-out are separate distinctions the can be applied to
any standing rib roast, regardless of grade.



  U.S. Prime – This is the highest grade of beef with the most fat
  marbling. This meat is very tender and only accounts for about 2.9% of
  all graded beef. U.S. Prime is usually reserved for high end dining
  establishments. Because this beef has such a high level of fat
  marbling, it is excellent for dry heat cooking methods. from: http://foodreference.about.com/od/Meat/a/Usda-Beef-Grades.htm


Also, technically a Prime Rib is not a 'steak' but rather a 'slice of roast'. If one takes a slice from a raw rib primal and grills or broils it as a steak it is a "Rib Eye", and can also be either "bone-in" or "bone-out". (the use of the word 'primal' refers to a primary cut of beef, the first cuts a butcher will use to section a beef beyond quartering, it is utterly unrelated to the word "prime" in "Prime Rib" )



[Edit 12-21-17: Additional research indicates I had causality inverted. The USDA choose the term "Prime" because of the popularity of "Prime Rib", a term that apparently existed before the USDA grading system. More importantly the 'Prime Rib' is cut from between the #6 and #12 ribs, but may be of a grade other than 'Prime'. However, the initial point remains true that "All Prime Ribs are standing Rib Roasts, but not all Standing Rib Roasts are Prime Ribs". The 'Standing Rib Roast' may include (or be exclusively) from outside the 6-12 range. The potential difference being from where within the rib primal the roast is cut.]