Within the Systematic Theory of Success there are a number of factors, grouped together there are potential, kinetic, control and physical kinds. This is a complete list and explanation of the potential factors.
People with a sense of purpose are not directionless, unsure of themselves, or being pushed around by life. They know what they want. They must have become self-aware at some point in their life and worked out what is important to them. Many parts of their life just seem to fit in and belong to that purpose. The more confident that person is the clearer you see how different aspects of their life fit neatly and fulfil that purpose. If you were to describe that person in a sentence you are likely to describe just the purpose alone and what they stand for, not just by some common definition.
Logically having a purpose makes it clearer what direction is needed to achieve it. The confident person appears to know where they are going. Often a trait associated with achieving anything in life this person knows already what it is they are going to do. If you think about how this person will be spending their time generally then you answer will likely contain the direction they are taking. Is it possible to have purpose without direction? This probably occurs if the confident person has newly acquired or changed their purpose and not worked out the details. Think of experience as a teenager, purpose without direction seemed to be a common problem and a lot of energy usually appeared with nowhere to go. Without direction the confident person would appear more like a dreamer.
Belief is the certainty of knowledge. This is probably the defining factor for confidence, when you see the others you recognise they are also traits of successful people, but this one alone if removed will prevent a person from being confident. Having purpose and direction is of no use if you are not sure you can do it. Certainty of being able to achieve your purpose and continue towards it is imperative. It is connected to the other potential factors by strengthening them. Without this certainty, or belief, the purpose and direction can exist but they will be very weak and can be subjugated by other factors, like fear. Alternatively, belief without purpose or direction could not logically exist, for example, what is it that you would believe? Belief is not strictly knowledge, but the certainty of it, that the information in the knowledge is true.