Directory - Is accessed from the IVR by Selecting "Enable Directory" checkbox
When a caller is in the IVR they can press # to access the names directory.
The directory is built from the information that was entered during the creation of the extension and voicemail. For basic look up of extension names this is all you need to enable.
The option to choose searching by first,last, or first and last name is configured from the General Settings under Company Directory
Phonebook or Asterisk Phonebook or Phonebook Directory is a completely different option. The confusion comes from the naming.
There are two install modules - Phonebook and Phonebook Directory
Phonebook appears in the Tools menu as "Asterisk Phonebook" once installed
This is where you can create your own phonebook entries
Phonebook Directory is found in Destination options of FreePBX once installed. In the IVR you can select Phonebook Directory to search for names that were entered in the "Asterisk Phonebook" under the FreePBX tools menu.
This can be used to dial other names besides extension names.
*Note: The Asterisk Phonebook can also be used as a source for Caller ID Lookup Sources Module