notification form; registration form
A formal written document submitted to a government office or authority to notify or register something, such as a change of address, business registration, or tax filing.
When you move, please submit a notification form to the city hall.
Please fill in the required information on this registration form and affix your seal.
申請書 is an application form for requesting permission or approval, whereas 届出書 is a notification form for reporting facts or changes, often without requiring approval.
Compound of 届出 (notification, from 届ける 'to deliver/report' + 出る 'to come out') + 書 (document).