Promise - we make it to others & self in our day-to-day life. We assure people about some task we will accomplish. We swear to complete some assignments. We give our words to people about doing something. Promising is one of our trait in day-to-day life.
But commitments are meant to be kept & completed. Commitment is one of the qualities of a great leader. But this question is about the perspective of promise itself. In our perception, we generally make promises to others. But do others get affected by our promises? It is our will - that get added to or decrease as we keep or ignore our promises.
As one keeps his/her promises, one's will power increases. It adds to our goodwill & our strength if we accomplish our promises. May it be to others or to our self, promise when completed - it gives us a sense of accomplishment - a sense of achievement - a positive increment in our will power. So in true sense, it is us who get affected by our promises - be it to others. If ignored, our self-confidence decreases - it may not be clear - but it hampers our growth as a leader. So in this light - promises are always made to self - it is just in language that we make it to others.
Commitments are a part of living - be it quitting a bad habit, accomplishing a goal or doing something for others. In language, we make many promises to others - but ultimately it is us who keep it or ignore it. In this light, we must understand the perspective of above question to live better & gain self-confidence with each accomplished promise :-)