What is the relationship between self and personal identity?

Personal identity is a subset of the larger concept of self.

Personal identity refers to those attributes of a person that make her/him different from others. Self refers to the totality of an individual’s conscious experiences, ideas, thoughts and feelings with regard to herself or himself. These experiences and ideas define the existence of an individual both at the personal and at social levels. Therefore, personal identity is a specific aspect or subset of the broader concept of self, focusing on the qualities and characteristics that define an individual and set them apart from others.