If we wish to establish a presence or engage in some activity in a virtual world, we have to somehow transpose our consciousness from 'here' to 'there'.
The final step of this transposition is usually a creation of a virtual self in the virtual world, usually retaining basic characteristics of ourselves we have gotten used to in the 'real' world.
So far, I have seen three terms which are in use to describe the virtual self: avatar, character, and toon.
There are subtle differences to the use of each.
An incarnation (virtual body/self) of a god (player/user). An avatar reflects most clearly the ('real') self of its user.
Honestly, I haven't seen in-game virtual selves referred to as avatars much. This probably doesn't happen because we don't really want to be our 'real world' selves in-game; they can be burden enough in 'real life'.
The word 'avatar' is mostly used for a depiction of a user's account on a forum. The avatar pictures seldom reflect anything of substance, but the posts on forums are usually the opinions of 'real world' selves and not virtual ones.
One of the definitions of the word 'character' in my dictionary is: "the aggregate of features and traits that form the individual nature of a person or thing". This is a good enough definition in this context.
The word 'character' is used most in reference to virtual selves.
If there is such a thing as an 'intrinsic' or 'true' self, a character would be a representation of such a self in the game world (bound by its rules) as much as 'real world self' is a representation of 'true self' in the 'real world' (heavily influenced by its social rules).
We embody various aspects of ourselves in in-game characters, perhaps some of which we can express in the 'real world' only with great difficulties.
The original definition is "a character in an animated cartoon".
I don't like to use this word. It stands for whatever the word 'character' stands for, but in a much more 'flattened' version: The virtual self is reduced to an aggregate of numbers in the virtual world.
Toons are mostly seen simply as outside tools, bearing only the bare minimum of self-identity.
As a well-rounded and useful word in the context of virtual worlds, 'character' gets my vote.