There is an overlap in words and meanings. Ego and evod can mean 2 different things.
Fist and most basic is what Izan posted
An ego style battery has a 12mm threaded shoulder, it has a 510 connector in it's centre.
Look at what the arrow is pointing at. Those outer threads are what is meant by the ego connection, but ego connections have the inner 510 connection also. The original battery to use ego was Ovale (ETA - pictured below is an ovale twist which isn't the original, I just put it so you see the overall form factor)
That style battery became known as an ego (even when made by others) but as noted, the connection threading is what makes it an ego (now).
Many battery devices use the ego threading.
Evod is actually both a battery and a clearomizer (atomizer). Usually people say it as evod kit, meaning both the battery and clearo, or they say evod battery, obviously meaning just the evod battery. Usually when people just say evod they mean the other picture from Izan, just eh clearo.
Bottom line, yes the evod (clearo) will work with your ego battery. Yes your ce4 type clearomizer (I'm guessing that is what you referred to) will work on an evod battery also.