In Wicket, a Person can have a relationship to an Organization, and/or a Relationship with an Organization. While both of these connect the Person to an Organization in some manner, they have different meanings in Wicket. Updating one will not update the other.
When a Person has an active relationship to an Organization, this means they are connected to this organization for example, as an Employee. The relationship can have a Start and End Date, so if their employment changes, you can end the relationship.
A membership assignment on a Person record means that their Organization is currently a member, and the Person has been assigned membership via this Organizational membership. This is separate from a Relationship, and can have its own Start and End Date.