Self-consciousness is knowing what you are doing at the present. While self-awareness is being aware that you are conscious.
Animals are only self-conscious while Humans are both self-aware and self-conscious.
Self-consciousness can be attention seeking, it is external in nature. You are in a function enjoying every moment of it, the host calls you in to the stage to give a speech or to sing a song, suddenly you will become attentive and all your joy is vanished and now you come to consciousness and thoughts starts to flood in your head and you are consciously seeing all the thoughts. You started to think what other people in the function will think about your performance it will lead to worry. All the happy hours are Gone with the Wind.
So being only self-conscious is not sufficient to lead a happy life, it is equally important to know the values and characteristics of the inner self. Only when you are self-aware then only you can handle all the situations.
A monk who will never worry about any of his external need can only look inward, the external experiences will never make him to think for a minute, that is why he will lead a peaceful life.
While an ordinary person who is involved in all the external issues, should be very careful because he should be attentive about both internal and external issues.
Self-consciousness only helps us in knowing the present moment but self-awareness helps in responding to the situation in calm and peaceful manner. This will help in maintaining the peace both inside and outside.