It can always be difficult to prevent becoming confused by the huge variety of new terms that we use in the study of literature. From what you have written beneath your question, however, it seems you already have a good understanding of these two terms. You are completely right in that when we use the word "tone," we use it to refer to the attitude a writer takes towards a subject, a character, or the audience. This is normally conveyed through the writer's choice of words and the details that he or she stresses. We can normally describe the tone in one or two simple adjectives, such as affectionate or disgusted.
When we talk about character or characterisation, this is of course linked in with tone, as the characterisation of a given person is the process of revealing the personality and traits of a given character. Of course, one way that an author can do this is through the tone they adopt as they introduce and describe the character. For example, if we consider Sydney Carton in A Tale of Two Cities for one minute, even though he is described variously as a "wastrel" and as somebody who has wasted his talents in debauchery, it is clear that Dickens describes him with absolute sympathy and empathy through the choice of words that he uses and how he describes various scenes that show Carton in a sympathetic light. The tone is therefore key in terms of how character is developed.