Technically, the term Prime rib is a rib roast that is USDA Prime beef graded and has little or nothing to do with it being bone in or boneless. Most of what you will find in supermarket meat counters is USDA Choice and Select. In the not so distant past most of the PRime grade beef was bought up by hotels and high end restaurants and steakhouses. With the downturn in the economy the demand is lower so there is more prime beef making its way to main stream meat markets like Costco and of course your local butcher.
My understanding is a standing rib roast is just a rib roast with the bones attached, or, bone in rib roast. I have talked to quite a few butchers and what I've found is there is little consensus among them on naming standards across the entire cow. What one butcher calls a boneless rib steak another will call a ribeye or Delmonico steak. What one calls a NY, another will call a strip loin while still another will call it a KC steak. Sometimes it has to do with what the butcher trimmed off or didn't trim off that makes the difference in the name. Sometimes it just means one butcher was taught one name while another was taught something else and that is what makes its way onto the meat label.
The entire meat industry seems not to be overly interested in coming up with naming standards for the various cuts which means the consumer has to be more educated in what they're buying.
I'm going to be the contrarian here. I typically cook prime rib prepped like Deb does on the Big Green Egg very hot (500+) on a rack (bone down) in a pan with some liquid for about an hour or two. It sets a really tight crust that way. I'll finish it in a low oven (love the smell in the house!). Use the pan drippings for sauce/gravy. Works for me and I've not had any complaints or many left overs either.
I did my first bonless prime rib last year for Christmas eve dinner and the family has DEMANDED one again this year.
They are relatively easy to do.
Scooter was my mentor.
I pulled it at 135 and tented, monitoring the IT temp throughout the rise.
I took about 40 minutes to peak at something like 142/143.
The roast then maintained that temperature for about ten minutes before it show a very slow reduction in temperature.
I would recommend that cooks allow 1 one hour rest & relax time from -removal from cooker - to slicing.