Contact can have only one Type at a time
When creating a new contact, Contact type is a mandatory field with a dropdown to choose from the existing types.
For an existing contact, the Contact Type can be updated on the contact details page
Contact type can be assigned from the "Update Contact" action in Workflows.
Navigate to Settings > Custom Fields and search for "Contact Type" and click "Edit"
Use the "Type" filter in Smartlist filter to effectively create and save different filter views for different contact types.
