Non-Registered Users are those who haven't made a Chatango account.
More information here.
An Anon is the first thing you log in as when you open a chatango chat. It's a user that has the word "Anon," and then a 4 digit number after it. (For example, Anon1234.) Very basic.
Anons do not have profiles or pictures and are restricted to links only because the picture links will not embed. They also cannot use colors or font size, though they are able to make their fonts bold or italic.
Temps (short for temporaries) are almost exactly the same as anons, the only difference being that the name is customizable.