The Notifications option under an app's info in the Apps settings takes you options allowing you to restrict the app's ability to create notifications. The options shown here are equivalent to the per-app options available from the Notifications settings.
Prevents this app from creating notifications at all. The app will not have the ability to place anything in the notification bar at the top of the screen or on the lock screen, or to sound a notification sound.
Allows the app to create notifications, but prevents notification sounds or vibration. Notifications will be silent.
This does not prevent apps from making sounds in the background, such as when they are music or audio players.
Override Do Not Disturb
Allows this app's notifications to appear, including making sounds, even when Do Not Disturb mode is on. Do Not Disturb is an optional mode which can be configured to mutes or suppress notifications and calls during certain times or when manually activated.
Some apps will show additional notification settings, accessible by a settings (gear) icon. These settings are app-specific and provided by the app.
A well made app will usually allow you to show or hide certain types of notifications, providing a level of granularity not possible by outright blocking notifications using the above settings. If an app offers its own notification settings, it can be useful to try using those first.