Yours is obviously a bit thinner, and less marbling / fat. https://www.turnerandgeorge.co.uk/products/bone-in-rib-eye?variant=40118074245179
Yeah, I think you're right about it being rib having looked at photos online. So ribeye is this cut but with the bone and less meaty bits removed? It's the bit in the middle?
The rib eye is just a particular section of the rib where you get a nice nugget of fat running through mate. Doesn’t run through every section. Every rib (and there are a few) doesn’t have a rib eye.