Self needs Other(s) to exist, and Ego needs Other(s) to ignore. So Self is existence, and Ego is ignorance.
Self indicates subjectivity, and Ego points to superiority. Subjectivity is the expression of the factual reality, and superiority is the manifestation of the illusive reality.
One needs to understand his or her Self in order to be himself or herself, and one needs to realize his or her Ego in order not to be self-centered.