The secondary password can be the same on every server. However, changes that were implemented last year now require at least one numeric character in a secondary password. So, if you've recently created a new account or character on a server other than one where you originally started, you will be required to use at least one number in that password.
In addition, if you ask Support to reset your secondary password on a server/account/character, you will have to use at least one number in the new password.
Hope this clears things up a bit.