How to use the contact list in PrivateMembersData ?

The two are not connected so they will not show any changes.

You have either added Wix Videos app or Wix Music app to your website which has created those custom fields automatically in your contacts.

Or you have simply created new custom fields in your Contact List like here.
https://support.wix.com/en/article/adding-custom-fields-to-contacts

This means that you can now save user inputs for those fields in the Wix CRM in a user input form that you create.

The Members/PrivateMembersData collection is the collection that gets added automatically when you add the Wix Members app to your site and you can’t create anymore new fields in that collection.

Also, it is only the specific site member who can see their own data in the Wix Members collection.
https://support.wix.com/en/article/corvid-wix-members-privatemembersdata-collection-fields