This is the Spotted Moray. Its probably our most common moray - we also get the goldentail and green morays regularly. It fits somewhere between the two - bigger and bolder than the goldentail but nowhere near the bulk of the bigger Green Moray (which is up there with the biggest Gymnothorax eels)
Its a little slenderer than some other Gymnothorax eels of a similar size and seems (in my opinion) to have a slightly more relaxed disposition.
These are two different animals by the way - the top one is Antiguan whereas the bottom one appeared free swimming a few inches underneath me as I photographed some angelfish on a local site!