As described before, "outlaw" can either describe a criminal or the action of making something illegal. However, ban can also be used in other contexts.
In online forums you will often hear about people getting "banned," which means they have been "kicked out" of the group, due to breaking the rules or otherwise inappropriate behavior.
So, "outlaw" is almost always used in a legal context, but "ban" isn't necessarily always used that way. I think of "ban" as meaning "to block" someone or something, rather than making it illegal.