“A postback is a request sent from a client to server from the same page, user is already working with.“ASP.NET was introduced with a mechanism to post an HTTP POST request back to the same page. It’s basically posting a complete page back to server (i.e. sending all of its data) on same page. So, the whole page is refreshed.
A callback is generally a call for execution of a function after another function has completed.” But if we try to differentiate it from a postback then we can say: It’s a call made to the server to receive specific data instead of whole page refresh like a postback. In ASP.NET, its achieved using AJAX, that makes a call to server and updating a part of the page with specific data received.