A notification payload is the incoming data which will be distributed to any of your configured channels. You can use the default payload which will work for most cases. If you want to enhance the notification you need to provide all necessary custom data in the incoming payload.
With push.delivery you are able to customize your notification on any channel. Your are not limited to a strict set of fields and can support mostly any use case. The incoming payload (JSON) can be contain any data which will be mapped/transformed into the specific channel/app target format via the transformation language Jolt. Future modifications are possible by just editing the channel/app templates.
In case you just want to use the default push.delivery format then you only need to fill and send the incoming payload and don’t need to change the default Jolt templates.