There is a slight difference. Safari supports two types of notifications: HTML5 web notifications (since Mountain Lion) and Safari Push Notifications (since Mavericks). The difference is not really apparent to the end user, because they look the same and both show up under "Notifications" in Safaris preferences. However, HTML5 web notifications are standardised and work across all browsers that support the standard, whereas Safari Push Notifications are proprietary and only work in Safari.
Safari Push Notifications are treated as separate services in the Notification Center, whereas regular HTML5 web notifications are simply part of Safari. You can easily see this when you run these two tests:
https://dangercove.github.io/html5-notifications/ (HTML5 web notifications)
https://zeropush.com/safari (Safari Push Notifications)
You can see the result in the attached screenshot. HTML5 web notifications show up under Safari notifications, whereas Safari Push Notifications have their own item. This means that all HTML5 web notifications will be affected by your notification settings for Safari. So if you turn of Safaris notifications, then you wont see the upper notification anymore.