Xero automatically assigns contacts as suppliers and customers as soon as a bill or invoice are raised against them. If you look at the Contacts and think that suppliers or customers are missing, the contacts are there, but just not yet categorised as there are no bills/invoices raised against them. Just search for that contact in 'All'.
Xero does not allow for duplicate contacts, however, some software packages require the contact to be entered as both a supplier and a customer. If you have this scenario both contact entries will be added with a unique identifier added to one duplicate contact.