rib on the bone = côte à l'os
Just a word to add to the discussion: as a professional translator, I am frequently required to translate some of these beef cuts with technical accuracy, and quite apart from the differences between English and French butchery, it's also important to bear in mind that the French terms themselves are sometimes used quite imprecisely, AND there are often several different names for the same cut, often with a degree of ambiguity. hence why so many of the diagrams we see may seem at times to be incomplete or contradictory.
French customers, too, are not always as clued up as they may at first seem!
One name that gets a lot of people caught out, and is quite important to get right, is the important difference between 'bavette' and 'bavette d'aloyau' — which despite the similarity of the names, are actually totally different cuts. I was luck that my former boyfriend was trained as a butcher, and so was able to explain very well how the cuts were differentiated; and as he was also a top chef, he knew how to cook them properly too!