All true eels have a laundry list of readily identifiable characteristics including:
- elongated bodies
- a snake-like appearance
- no pelvic fins
- doesn't have pectoral fins
- no gill cover openings
- no scales
- continuous dorsal and anal fins
- locomotion via flowing, undulating strokes
- mucous covering for protection against abrasions
Moray eels, in particular, have lateral line pores on their heads. This allows them to hide in crevices and caves with just their heads sticking out while still being able to sense movement in the surrounding water.
In many cases the creatures characterized as “eel-like” fish have none of these special adaptions, but they do have elongated bodies. Because making these distinctions can be very difficult for all but the experts, I am choosing to go with more simplified language.