You mean a simple notification, which is triggered by alarm (specific time)? In Android there are no different words for push/local notification, because a push doesn’t automatically trigger a notification. A push triggers an intend and it’s up to you what to do: show notification, open app, delete contacts… And an alarm (in Android) also triggers an intend, where you can decide what to do. The only bad thing about an alarm is, that you have to add it after device reboot again, because they are not persisted.
Sorry, but I don’t know the iOS way of doing it, but I know the wording local notification from the iOS world.