yes, prime rib is the most common type of steak in the US.
I am sorry i didn't make it clear, i was talking about the "beef small rib" (word by word in Chinese) i have never seen that type of "prime rib"
Usually, when people buy Prime grade, they buy steak. I can tell u an example and i think it would be easy to understand.
Toro is one small part of Tuna. ONLY that small part of Tuna can be called Toro. If the meat is from another part of the SAME fish, it would be called Maguro (regular tuna, Maguro is Japanese)
HOWEVER, people sometimes don't care so much,or business men want to make more money. They basically call Toro to other parts of Tuna fish. I have seen Toro fish head. Grill Toro tail... and so on... In my opinion, i think it is misleading and simply wrong.
If you apply the same logic into beef. When this cow has one part graded Prime. It doesn't make the whole cow prime grade. (very often, The SAME cow may has prime grade rib-eye but choice grade NY strip. The grading is not depends on the cow, it's depends on the meat. Think of this like an Apple Tree. not ALL apple on the same tree are top quality, rite?) However, If someone marketing the other "not prime" parts as Prime grade. It is misleading.