First of all, the definition of "fish" is: vertebrates that live in water all their lives, breathe through gills and swim with fins.

Fish include the three major groups of the class Ophiuroidea, Chondrichthyes and Scleractinians. There are more than 26,000 species of fish known in the world, which is the most diverse group of vertebrates, accounting for 48.1% of the total number of vertebrates. The vast majority of them live in the ocean, and there are about 8600 species of freshwater fish. There are nearly 3,000 species of fish in China, of which about 1,000 are freshwater fish.

Then for eels do belong to the fish, only the distribution of the program is different. Eel, also known as eel, although no fins and scales, but it is mainly with gills to breathe, so eel is a fish, belonging to the order of fish gill. By the same token, the loach has fins without scales, mainly with gills to breathe, so the loach is also a fish, it belongs to the order of fish carp loach family.