On-site notifications are live messages shown within the Notifications screen. They show up to let you know about the changes or updates on the site you subscribed to, or the system messages sent from AskGamblers.
Email notifications are messages you choose to receive in the form of an email. Whenever there's a change or update about the something you subscribed to, you'll receive an email.
Desktop notifications are pop-up messages within the browser you use. They show up to let you know there's a new message for you even if you are not looking at the site.