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Both the Do not Disturb mode and Focus mode are able to control the notifications from specific apps. When either of these modes are active, blocking notifications, clearing away any open notifications from specific apps, and stopping any further notifications from showing up, all become enabled.
In addition, the Focus mode will also block the offending apps from accidentally opening. When Focus mode is on, you won't get any notifications and won't be able to use those specific apps which are selected in the settings.