How to bind contacts to another apple ID I have two iphones who were using the same apple ID, so they had the same contacts and this was not ok, because every iphone is used by a different person and we want to have different contacts. So I created another apple ID, and I logged with that account (settings->itunes store and app store->changed the apple ID and verified it).  

But even if I changed the apple ID, the contacts seem to keep being bound to the old apple ID, so that from an iphone I can change the contacts that are displayed in the other.
If the contacts in question are coming from iCloud, you'll need to change the account in Settings → iCloud to a different iCloud account.

Your contacts may also be coming from a different account (or multiple accounts).  Check other accounts in Settings → Mail, Contacts, Calendars to see if any of them may also be a source of contacts.