Note in the above definitions, it is not a requirement that something be TRUE for it to be a belief, only that an individual accepts it as such.
Words have meaning based on context.
In communication, it is the obligation of the originator of a message to ensure that they say what they mean. They should also be sure that their message is worded clearly and in a form understandable by the person(s) they are communicating to. Most people are not very good at this.
It is also the obligation of the receiver of a message to try to, in good faith, understand what the communicator is trying to say. Most people are also not very good at this.
When you consider these facts, it's amazing that we ever get anything straight.