When viewing an Advanced List with Emergency Contact information, the field Emergency Contact.Relationship only seems to output the title of a relationship for some users, but not for others. Instead "Has Relationship" displays.
When a user shares a relationship in the system with the user who is listed as an Emergency Contact, the phrase Has Relationship will appear, indicating that these users have a relationship. When a user is added as an emergency contact but they are not in the system, then the relationship that is manually typed in is what would display. This is also why you may see differences in how the relationship titles display, such as Grandmother, grandmother, grandparent, etc.