Admins decide on the notification options that are available to users in Administration > System settings > Notifications. Admins can activate these options, but it is up to the users to enable them in their Notification settings. Notifications are always set on an individual user level.
If an option is deactivated, users will not be able to see or enable it. For users to be able to manage their notification settings, they require the "Manage notification settings" and "Access notifications" permissions.
The options are:
For push notifications, admins can choose whether push notifications show a short preview of content.