The following is largely from a previous set of answers I have given to a similar question.
The common native American eel, Anguilla rostrata (brown or yellow eel) begins life in the Sargasso sea, migrates to costal bays and river mouths, remains small there, and then migrates up rivers and streams to reside in ponds and lakes for years, growing to adult size and then migrating back to its breeding grounds. Eels can and do sometimes migrate some distance over dry land from stream to pond. During their fresh-water life, eels grow considerably larger in northern waters than in the South. Females grow larger than males. Eels are carnivores that specialize in live crustaceans, small fish, etc., but will eat any meat, living or dead. In small numbers, they are unlikely to have much impact on a pond of an acre or more, I think, and they cannot reproduce in fresh water. They are toothed and can give an unwary fisherman a nasty bite.
On the other hand, exotic species which can reproduce in fresh water have been introduced to American waters from time to time and have the potential to do great damage. You will remember the northern snakehead scare in Maryland a few years ago. Also, so-called "rice eels," which are air breathing fish that look like eels but are not and that can migrate long distances over land, have been introduced into North Georgia. Unlike the American eel, they have no pectoral fins. They would be almost impossible to eradicate once established.
If you still have the fish and are not absolutely positive it is a native eel, you would do well to have it identified by an expert.
Lou