What's the difference between Directory Departments and People Departments and how they integrate in Cliq?

What's the difference between Directory Departments and People Departments and how they integrate in Cliq?

In the Remote Work section of Cliq, you can filter Cliq users by Department. However, none of the Departments I have created in Directory show up here. Instead, it's only the Departments from People.

Should the Departments in People be in sync with the Departments in Directory?

Can you choose which Departments are shown in Cliq?

Thank you.