The eye of the rib steak is probably, in my opinion, one of the finest grilling steaks available. Enjoy! I will admit to finding a rib steak, bone-in, to be a bit more flavorful. Ribeye, bone (flavor) removed, rib steak used to be universal in meaning. Butchers, I don't know the reason, in different locations have so mixed the names that they are meaningless to most of today's butchers, retailers and consumers. To me though, they distinguish two different cuts. Sadly, perhaps, I've become too old and too critical. But, I do remember a time when "words" had meaning.
The worst change was when "Prime rib" cam to mean any standing rib roast. Used to be a "prime rib" had to be graded prime. Now days one needs to tell the butcher that a standing rib roast graded prime is desired or, one pays a premium for a stander or, perhaps better, will be served up. Buyer beware! Again, perhaps I'm to set in my ways.