Display-Name vs Display-name-printable

Greetings,

AD has two 'display name' attributes: 'Display name' and 'display name printable'.

The Public information property set allows write to the 'printable' attribute but not 'display name'. Does that mean I have to set the write property permission for the display name separately or are they both the same thing i.e. if I give the write permission to 'Public information' they will also have the permission to modify the display name property?

Thanks

David Z