The difference between Hierarchical Relationship and Self-Relationship are as follows:

Hierarchical relationships

• A Hierarchical Relationship is a special type of lookup relationship which is available only for the user object.
• A Hierarchical Relationship allows users to use a lookup field to collaborate one user with another user without reference to itself directly or indirectly.
• A Hierarchical Relationship is Self-Relationship of the user object.
• For example: We can create a custom field with hierarchical relationship to store each user’s direct manager.

Self-relationship

• A Self-Relationship is a relationship when an object lookups with itself.
• A Self-Relationship creates a tree diagram of the objects, like an account has a lookup with himself, called Parent Account.
• A special self-relationship of a user object is known as a Hierarchical relationship which helps to create superior roles like a supervisor, manager of the user object.